2/4 Automorphic forms for GL(2)
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Formal Metadata
Title 
2/4 Automorphic forms for GL(2)

Title of Series  
Number of Parts 
36

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  
Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2014

Language 
English

Content Metadata
Subject Area 
00:00
Point (geometry)
Group action
Finitismus
Existence
Presentation of a group
Direction (geometry)
Real number
Distance
Mereology
Area
Causality
Manysorted logic
Lecture/Conference
Natural number
Square number
Hill differential equation
Condition number
Spacetime
Military base
Element (mathematics)
Set (mathematics)
Sequence
Equivalence relation
Computer animation
Lattice (order)
Game theory
Family
Matching (graph theory)
Local ring
06:51
Principal ideal
Musical ensemble
Presentation of a group
Multiplication sign
Decision theory
Direction (geometry)
Mereology
Rule of inference
Number
Subset
Quadratic equation
Goodness of fit
Manysorted logic
Lecture/Conference
Square number
Hill differential equation
Social class
Condition number
Spacetime
Closed set
Voting
Graph coloring
Finite set
Figurate number
Kongruenzklassengruppe
14:30
Point (geometry)
Addition
Complex (psychology)
Presentation of a group
Real number
Multiplication sign
Tournament (medieval)
Content (media)
Mereology
Number
Subset
Goodness of fit
Crosscorrelation
Graph coloring
Vector space
Lecture/Conference
Wellformed formula
Order (biology)
Kongruenzklassengruppe
Descriptive statistics
Local ring
24:22
Addition
Group action
Existence
Spacetime
Presentation of a group
Observational study
Latin square
Mathematical analysis
Sheaf (mathematics)
Set (mathematics)
Local Group
Frequency
Arithmetic mean
Goodness of fit
Vector space
Order (biology)
Table (information)
Family
Condition number
Social class
31:44
Point (geometry)
Group action
Musical ensemble
Observational study
Presentation of a group
Decision theory
Distribution (mathematics)
Valuation (algebra)
Mereology
Food energy
Frequency
Goodness of fit
Strategy game
Manysorted logic
Meeting/Interview
Lecture/Conference
Forest
Square number
Integer
Units of measurement
Position operator
Condition number
Addition
Focus (optics)
Spacetime
Military base
Projective plane
Moment (mathematics)
Basis (linear algebra)
Mathematical analysis
Algebraic structure
Set (mathematics)
Functional (mathematics)
Sphere
Vector space
Lattice (order)
45:15
Axiom of choice
Presentation of a group
Multiplication sign
Distribution (mathematics)
1 (number)
Infinity
Set (mathematics)
Weight
Functional (mathematics)
Heegaard splitting
Inclusion map
Equivalence relation
Meeting/Interview
Lecture/Conference
Phase transition
Family
Position operator
Condition number
52:57
Principal ideal
Presentation of a group
State of matter
Multiplication sign
Distribution (mathematics)
Complete metric space
Inequality (mathematics)
Sign (mathematics)
Population density
Manysorted logic
Positional notation
Lecture/Conference
Term (mathematics)
Natural number
Social class
Area
Spacetime
Eigenvalues and eigenvectors
Forcing (mathematics)
Functional (mathematics)
Summation
Lattice (order)
Quotient
Module (mathematics)
Gleichverteilung
Figurate number
Resultant
00:03
Hey if a
00:07
world and so I stuck poultry so I see that they you definitely goes through and beach so that the open won't lose Virginia Moss also to avoid this may be the will of the people with what we have done the distance so however that make goal was to investigate this thing I principle which is is to date back to 2 2 they mind to reject stands the effect of a halt presentation of new pages by your request that it from being elected he is not meant to be and so we have the sort of natural candidates of for equivalent of 4 creatively on 404 for which is that with well I could so he that this is a by 2 and the year this is his statements of which is a bit longer but which element that he which so but that's soldiery question so we want to resolve the situation through heat .period the sole here we ask for the new solution to the situation in the that and here we have we asked whether a solution to the situation in the thick of space earned in any of the real cause of lattice is attached to a friendship we we say deal is brokered the hawkers on the and I use In a until the road was due to leave sufficient condition for this to and so I just stated that the generalities and so we could do more to study this question and especially to study this condition we have been told you the of that season which after losing the related to Seoul which was gorgeous the the security use of and the from is the effect of lettuce is so a crime of questionnaire alleges which look at is only 2 and as always as I have explained to the sector can be realized as as not being part of the letters back and direction of some when so he is off to a world October 9th goal of the square that the firm and so g of air is both at the point of finite Billy Bonds which is a set of sequences he left the game in hills cubicle OK and the he please call on the air so because we have this because of that scandal completely legal bases by you is that all future collection of local electricity is we can act on each local elections using and create new so so in a sense why but why this set of Virginia's is is that you have to consider because when you are aware of the existence of such an action of the them season during a highly never walked on the space of the set of customer letters lettuces you see that the letters which In the future use of the after the exactly the same set of letters which satisfies the scholarship on any of these conditions that just because of the for different sectors of the nonempty Fossum fault and the then set will be in a nonentity if your place emptied by the end of local the summit at which so in a sense it demolished the most matches of the most naturalized set to go to college and when you look at these conditions must notify families affected and so yesterday and we finished on the consequence of the soul of so could you laughter as principal which is when you rule so there are some things but when you is the equivalent of 2 conditions like this where air the place juventus faced UN and aid if he plays by the
06:52
rules could affect of space to people to do so meeting together the consequence of this definition includes just a bit centurymaker gas just as the principal implies that year I have a high streets leading to the local news "quotation mark pleasantly but died a few years equivalent to the it is also presented by Hugh the so high so that the hill don't necessarily have a whole presentation in in the letters we want but we have a wonderful presentation in 1 of envisage closing that includes the later letters OK so that the user this is good but the OK so that is 1 finger is that loses soldiers the said the union of its 2 finite set of selected OK because because you can't make enough of so of 2 is in fine actors but as I as I explained to the public and not as part of a good said that at the dedication of new please but these said a few of the time is not meant to manner but this is the case here for any of the legislators which is is the real bad he adamantly to a crime so far the primetime this is the user is not always so hostile that he'll be off the elections so so all he said the question of hawkers on pending deal it does not say it's not about a crime but I have the honor is due back in the May figure and now we have weathered the storm that month and so we there for a week or so which said that you can't as a sector so of band classes in Virginia so that's set so so that's and maybe it will continue with the definition of 280 votes can you name it but said it may be noted HQ and scored 6 Q last cancel this Silverman often think of so of course agenda like that is that is the Silverman's should weakness of the class number of inadequate started from and when they don't we believe you felt that it had station of it's in the context of Anderson and should write books but before it is sold then if we say these and other political knockabout seemed to be going you could so and they had asked Clinton by all odds to find the man of the show so I believe that OK you as a condition but it gives you but you whether presentation in some of these lectures classes but maybe not someone you might wonder but there that there are only so many finitely the possibilities if there the sort in the colors of principal officials but at least in particular so last number of them Of the letter is 1 so if you decision your of air is a 2 2 draw by resuming the class of directive so which is used in the daytime acceptance by all and so there there are a number of of quadratic from for which this discussed number of these wonderful example when and is to feed off the new website to square quadratic farm To begin club aquatic
13:37
farms and in that way you because of your hands of 7 long about some of 2 square feet square and full square another example of this is another example of OK you deserve this union and quadratic farms soldiers 1 as class member from 1 to so OK so there
14:35
is a bit so beautiful but maybe I should take in the protest number this is a tough and 1 so that you know whether something too so maybe we'll just see if you will what that the initiative that is 1 case which is meeting this year and the year after you nations and so on and so the number may not be well that the 2 of you is a smaller and smaller when blaming based more on the of the soldiers to naturalize humanitarian battery and which might be due to the complexity of the quantity of endowments of the industry's none of them was 104 still on active to let it so you databases of of air and then you you from what the economy creates a new computer that got me into it so I really find it that's just announced that it would be OK and then sold of science Of the description in fact if it is in addition to the class number with which these include
16:22
a tour to Japan where the number of people who did this man do to the number of maybe part fact so it's very small but In during this and then Q put them with we under different from what the precise formula so opportunities make to to make some creativity assumption and the that spelled that it has to be maximized if jurors into account and that of its own surveyed statements so but although it should be in minus 1 so something like this that pretty quick recalled so is all OK so that you can use it to you basically cannot escape over that is something we both of the most junior high quality problems so you can take it they stated that the subscriptions accepted in in a few cases these are some of the ways of the soul of a it's so it is with a twist that OK nevertheless so that the could another issue to completely ignore the the issue of being the addition adopting different so even so all of this simplify things because the difficulty on the side so um I want to look at it so now I want to know explained to work to come to go to 1 of the and just for the sake of agreement that need yeah we he did so OK so I remind you what we have that we had a hawkish competition and in some that at time which was given to us by the Supreme principle and so we have at least 1 and we will start from the top presentation to build the new ones OK and and as a way to do this so we we consider the age is a sudden walls so we take exist everyday users of these vectors In his October 9th hole this is a Najib like some of the October 9 polls which he is enough of a national unity and minus 1 that about because it's the October 9 will produce "quotation mark patent when you face dates to October in bottle complement of of the victim good excuse so you we could use the Serbs war and now look at it the albeit so you don't know at this point of view of and you concede that suspected crimes to which is of course contains 2 2 with food and Pinewood Studios security of so and so that some matches the that In fact subset of of 14 what do you have and so on so what does it mean so you have that the statement said Hi prime climbed to 8 but a primer so which ejections the correlation of real colors of mapping the the content of local people but AM and so you have an appointment to the aged 3 times and time for the but now you have a question that Q this is a time of peace because of soul and if you applied age 2 it's so because it's Joyce containing them in order local is is that that excuse is it's a and of course if you will excuse me because it does not move at all so it means that you Q means that if you With the set of "quotation mark presentation of the but what is important here is that any kind of news that this is the 2 0 2 1 2 men who made the task of trying at the only because you have not elected by your United may preach you have back acted by the by the end of the tournament so will book shedding 1 associated "quotation mark presentation In a sense that the Empire maybe you may not be enough useful presentation but you could have gotten from the it's a presentation of acting in previous year by year blueberries OK so now you
24:26
go so let because you have a new ideas proposed by the sectors and kind can be known instead to use of of so when the means 1 it means that it's you you know to heat through .period Cross and reevaluate and then then they then you have experience through which which the GQ minus 1 the duel which is affected me to again so so what what you have is that so let's try to win so with that ,comma that spent time and out of these tragedies ,comma hope families of Latin season which is so I don't think it is generic and Virginia go you with that union both of values amid protests in Seoul it is the spot meet as a group bodies amid the class we are invested in which we have obtained over presentation in that we won so it's a bit strange because we stop talking about presentations of some of that day so we do not move the vector appealing moved elected but of course so you see that venue when you order we think can get in your presentation because you 1st it but this group and so that the user at the 2 to pull its soldiers out of order it is still sure In fact what would assure you that it is somewhat home because there is no reason to do that as a most space shareholders that any of that season's Virginia we show that so if you look at the start of a kind soul and ensure they sufficient conditions so that when you look at the this obvious and you Newport acted on the Virginia so what you want to show you that this support action that you should so when you hear in news business is a statement about the top of its dynamic statement you have a space on which rabbinical packed so it affects the space is an emotional space Virginia season with a new space under the section of the people because it's not and that you take a sample of of you all of the bigger and you look at not meeting this goal and you want to know because of the sheer complex issues 2 some maybe it's made the discovery in this way so you have a question social OK so this is is what they did at the but can so those who claim is that so what went so 1 needs so we suspect to what I have explained the beginning we need to shore that exists it's so at a menu so basically is a statement was about to be in the analysis of boards whenever they efficiently and satisfies set of additional condition and is hoping pines and so so what we need to show is that the so promised additional conditions under which were paid but that existed the Of existence of presentation Qiu such that the page has sold itself is going to become media and so it is said it seen example of where you may have an army which is not the whole way in which appeal you can excluded because of his Quincy but does not tell you much about the insects that is its existence so as an example where they were not aware as you move that that is going as far as the goods it is legal for example suppose that the of the shape the note the G 1 4 OK so then it should both you and the I need to know about such that you step on the presentations and that few of its notes and quotes not told then you say that it is the 1 that it's not so which is a very enunciated vector or so it is a whole presentation of the deal but just tabulation and is there is a chance for own at the age of these is the just the study days of the it's not because it's it's so stellar muted but this does not as the D 1 good goes to infinity so you you have some smaller public violated to being created but the Soviets can this can be solved
31:44
awful if you were hotly
31:46
referred additional assumptions that I don't know if you are not be wishing that he would be square feel we love the longer the valuation of ably primaries this history we not talk so I will ignore the services Miss technique .period so so the condition that he India and you can always find would hold presentation and if so so when you started all of which will be increase Geneva victim so many maybe not premeeting but at least we know where the money is legal .period this is because of the addition of and it's all that stuff so did the ancient will depend on the rest of the rest of the world because it's cute depends on the solely for the move and and again and you will avoid that situation and if you told us we move on to what went on the if you experience it is increasingly clear that it is it is up to the end of development this year and because of this is the list of of all yet but you have to choose so you have to check with the stew and if you look for 1 2 make sure that assumes the square feet then as that is the most with the intent of the we evaporate would definition of it because we have so it is not because OK so because there is it so In the case of exceptional square glasses so OK so what they will explain it is that there can be no such a statement that you could afford the forest bases would be so when we pull something stronger but in fact is albeit 1 project that there would be a we want to pull would distribute it means that we will have to integrate the offbeat but the longer attest function on and on that basis the soulful most basic functions of the 1 associated to desperate because you don't the nothing from there would be no problem but you have also this function which after a tactic which often can act as associated to guide them and in this case it may be that easy it the good thing bad square glasses you'll get like that will be the sole look like there will be nobody not yet but we do it will be the genomes of lobbied so you can at that sort of thing produced condition 2 In this socalled presentation of the exceptional square places will come from the socalled please do not expect column of of the field but that he you had a so all in all I have to to mold the his Club structure and you have to know the shape of the letters because then you need to know we just got there which OK and so you know I want to work so you can and you don't know that you have the conditions to remain the region a unit of the provisions of the region in the urine of arms sold I have but additional conditions yet so none of them is age with gold and he that if we feel good posture of of of that space but it it will avoid some of fine then sold some find places OK so maybe so there is a OK the so besides the you Johan that is a very nice place where the strategies implemented which opposes the idea of living but in which we it's it's so say a dynamic statement but there is a place where kids gets the dynamic and dozens of people in there and so when disaster did not hold presentation of an integer value quantity from when the study "quotation mark presentation of quadratic lectures you know I just can't quite agitated and so you you you can make it just exactly the same reasoning Seoul accepted but you will not consider carefully studied Idaho 4 point but spent the days of said that fund and and some of its invention is that I don't think there is a very show business someone has to go go if you want to get to it so it's a
38:30
dynamic man is somewhat distressed and so what may be 1 OK so that's what I want to explain maybe is how the service at the age of you to pull even sold even more precise statements so OK so so suppose now we have learned that from the option of and we have had the added sufficiently many of these reasonable under conditions and to ensure that we have the assets in the analysis of conceived by following the latter's incisions in the once a of this old man 1 can from all findings public such acts as a deposing Sharon so we know that there are fewer of them and OK the moment you saw what was that Of the victor and then sold it is that you for a tool to look at the position of the future so the most obvious 1 is please stay some of the presentations by the end of the 1 part and that is contained in in 2 plus of minus 1 it is a sign of and that's what is this thing so we have a set of vector also which states that you on minus 1 of fabric of thinking that you some announcement so the feeling is that is that the media all of the gambling really depending on whether the quadratic from his base in the Gulf English and so on this is a fixed space and so what you may want to look at this fall that used to live up to you and that is the addition of all is those that said the future of despair Of all officers and distributed into that the would OK and so by you with your hand is that Williams is much into space With phone the of the Soviet sphere and is is can identified the we sigh officials it can be the denizen of the of a single point at the beach and so you majority of fatally .period here and in danger of being obtained from space and so as such it's it's emerging so it's not doesn't need to be questioned its the failure that and so because this is a moment in space it's at here that Music sold which is enacted uniquely designed to get which comes from taking that portion of the energy of the 2 countries to and the focus over and no 1 has the following a quick distribution statements so it was OK technicians communications we'll fight isn't you of you and want so just to the side is set of policies in the office of the decision so it's OK Was this week with you we still have that on October 19 facts constituting the on their own on the set of aquatic OK so that is the set of the new effect of lattices which hoped that aren't all that Houston's glasses so you know about this set the focus on patients nonentity when the governor proposed additional conditions
45:15
and the issue which is that the whole time so it is equipped to do and isolate it is equal to the unity of man in the photo really he goes to infinity conditions so conditioned to grant that you take accepting the old and there are specific to what and when you buy the equipment computer so what's so to To date 3 1 2 2 2 compactly supported functions on the good continues complicated but it's no problem to my definition as she could distribution he said Paul and uh sold we assume that so I'm isn't OK then the year so if you take the view that the age of oral presentations made of debate you in the middle of letters that I of side of this year convictions the 1 hour and so you might well have shown With the family but refused to move so when the last June so far the large enough it will be well defined and the it Congress we are stewards of the image and this is valued for every so often the choice of 4 present at In a sense you all for being taken out of presentations as well as well you know someone who has yes yes independent it is during the summer 1 so I went and he was clear you may face as he goes along so maybe but then again you can make so Motorola because it would assure you can make something there souls of the socalled will depend upon the police nonIndians discriminants of that you discriminative look at you want to explain hello I want to explain how it goes this equipment provisions statement because I want them to bleed before that the call and so and so what explain OK let me and he could get my eyes to the ease of Phase and means that the Of the latter in GQ emitted into the air so this is this creates a bowl of chili and and the Soviets what we said in the beginning of this act on the set of 4 presentations seoul vendor which after splitting it into 1 of the Junge Union 1 of all OK so there is a definite Minnesota and this year union is final and it's evacuation of the on the definition to include New York so she visited the financial position of the center of the competition splits into a finite Union of got idea all so when we we analyze what some so let's look at the Union so we will speed into a copy to itself so this is what we we want to win so OK so
52:01
this is the 1st of these is a few once the she won OK so no what is the she its function and is payable loss but because of this identification of the but do you feel as the you can view the as a function on an easy and which is so on the Net which pipes note yeah I want
52:59
to explain to I want to explain to the Japan so this is a function which is right there in the Hamptons the clients and OK so and is the use of force competition but that function on that portion it you can do with whom as you but there are over 50 feet shape so we buy density that sign is of the will shape so side of let me said "quotation mark so it's something about to fall and at the end and the compactly supported function of so the space competition but the function portion of the narrated by the function of which AFP obtained which are made in young by years of age so then what we are looking at it some of these often Of the son of a gun Indiana I of In the and nature of 2 of the gunmen I he's I will have notation H note and that OK and and this week and you can just switch summation and he has some of the results of the trial of its knowledge of what could be of cannot you I don't know what to do now yeah well the people of them idea is that the function which is obtained by averaging about Denmark a few of them so when this is over phone which is continues contact you got understand quotient is what you get mad so so all of this that might buy what made them a new opinion in Spain so so egregiously mission statement 4 for presentation a few of the a few of the I it's equivalent to the unequal distribution statement so for what area of the state this is equivalent to what an equally provisions statements .period collection of H shares its notes of a house of this in the space the quotient the move you get so it's a storm that during the twoyear principle so and so she can you see we are looking for an equal distribution problems in the portion of the principal so now we have to many of 2 of the phone so OK but she here so it's a statement in innocence which was made the proposal for the man made false information in get my eyes always it's much better if you want to to apply to sort this problem is it's much better to look at it as an equal distribution statement cornichons on page note of this in the following days in the John OK and I will explain so I will explain next time but this thing is natural identified with the following quote shots so you take the time he said divided by the module is gold so of look at it and the soul and the locations of the Tolers beds plus the collection and collection of meat so what is needed is a collection of of these can be realizes that as as appointed on that portion of the of the h fair times age it has plans I would say that we to yeah said the a kind that we have so paycheck it added goal which was being produced here from my work created for presentation Seoul so when In a sense when we when we want to support democracy sizes of their chance of Issaquah distributions your and we have to look only at all the at the Goddard agreed distributing the space of classes of personalities but we we have to look at all the sort of complete obsolete equipment used in this league added caution and so to study the sacred distribution problems you have to analyze this caution :colon thank this is the beginning of the end government at the London meeting this morning not only it's what what would you think you're going to be in the hands of the lives of his views In the end I will not the most the worry of the that all of the no no it's not take your pick of the offer OK so when and when 1 end users for all these things can be interpreted in in terms of the about but not so obvious albeit it's here you can related to thousands of dilution comes from bountiful for eigenvalues figure of the fall in face this obviates is related to a function