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# 3/4 L-function

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#### Automatisierte Medienanalyse

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Hey if a and so
foolish begin by finishing this stuff could have the proof that essentially the argument that here or any so that so we want to I should just explained how 1 can evaluate the reason why they would come to give you this right powerful for over so let's look at that the left-hand side for so I can expand any kind of became minus 1 it would be a sample numbers up to so it kind of goes up to the summit and goes to acts so multiplied OK minus 1 of the most humble subjects so that he might want some kind of function which is like a device function with quality minus 1 and or idea and this function lets just say it's a number of ways of writing an on the part of a woman case where the jail most so now if I use this is not formula that we know that we can evaluate the 1st moment possible but so I can compute but the number of some his commitment of the blacks that this behaves like this assassin public to some constants Quicken which will forget some of and going to exit a minus 1 intent and then that's right and less than 1 times and 2 squared maybe where and when the square feet and when I get there From the form that we still have as the answer so we get something like 1 of more than 1 extends the the effects now to get this up about this a long on for the kid moments I only needed more money for this quantity Everything is positive so I can just focus on what what comes out I want and not worry about don't want that I don't have to worry about this is that at least make as big logic so this is not some next time slot and let's just worry about and that's less than than expert so that I don't have to worry about what decay minus 1 of Annex it's just became 1 of them so that these lodges and act the came 1 of them and then it's going to be divided by then and what times entered the spiral of and 1 and 2 so
this is essentially a multiplicative function so let's say well it has some of the functions of a minister I put the money into squares so you can see that this kind of roughly looks like excellent at some plants and 1 goes up to maybe tracks became minus 1 gold and 1 and won under the terms of the decay minus 1 and 2 squared Over and this is not strictly speaking because and 1 and 2 can have something in
largest number you can do in so this this sequence of numbers the edge of the Bj the increase was rapidly like the guy who was subsequently multiplying all the previous number many 1 but increased suddenly thought much faster than so now the idea is going to be there that we're going to some versions of these some of these functions b of Title VII of the for the zeta function taking shorter and shorter things but fall but police stopped parameters Biagi the beach at home explained and start with the degree of data have cited in the world L goes from 1 to 4 so cold case of Bell of the world I want to peace of mind the and days of Belfast is going to be the some of the of cable work Of over and the S and goes up to some small power the the tee the 1 was on it and then this be so well have minor it's going to be some of the OK over the years and from the again this and also some very small tomorrow for the ideas that is that this kind of stands for don't westerly can and this is the standard for was here for the staff have mine likely to the the sorry so when I'm by all of the powers of the House this guy is a for Zayed office product as standard for the half -minus IT to the case and this whole project it's like an approximation of the laws have "quotation mark came minus 1 so so if that is that and you should describe the water written down is kind of like a proxy for the 1st of the 2 but on the other hand the but on the other hand the girl shot dead 4 so let me explain to because the Chileans Guler separately to the wall 180 or so when you multiply all out still goes up only a predictive of 100 the same up to him he sought to shore up the 4 corners of the multiplied and then you can use holders inequalities have to say that this is prompted by the 2 the 2 of them I think you you just can't the part of the world of Montvale likely to lead 2 you can see if you don't believe that the quality of the strength of the exponents the 1 so that someone over to the sum of 1 or 2 aerial adds up to 1 minus 1 over cases those 2 things have to have some of the 1 or 2 appeals had gone to inequalities correct then you can you can again evaluate everything in sight because their function multiplied by 2 short football mills and this the shortage Maryland so everything can be evaluated and it gives you lot work to get more moment of which claims depends on the assumption that only depends on the ground that and doesn't depend want international approximations so let me just maybe roughly explained why that article result and I want to say this In March the day but the point is that showcases the feud when you think about this summer and to the detail as to what these people when you expand things like those of you who should know like I think we are making contribution was coming from the decay and square or an and going up to some up to some quite like gossip the that the constant binds the looked into the case square the fact that you from getting at something like 2 the 1 over 100 there might roughly that when you can yield some expansion like you might know something and have only those terms with them going up to some small power but what's the loss in doing this would be a symbolic something like a loyalty to the case square with the usual constantly but then divided by wealth is going up to 2 years undergoing a particular 1 100 Dale something like 100 failed so you you some constant which is going to be some power or some takes power on the air so we will suddenly lost something when doing this from but on the other hand I'm not using that the power 1 and using it only the part 1 or 2 so I I have some but the losses really going to be only the number 2 1 away to where I want most is not really a L looked like a to the
why we get the various powerful law in the distance in this moment conviction that to that we supposed to do so let me start with that With the recalling some books that I mentioned yesterday which says that if I so it recalled that it says that if I look at the longer they don't have a slightly thickened the real images of the look at the real part here and I supposed to varies between twice captained the team and quite quite that in this range this is approximately With means and what this means is that OK so that's that .period down so this means that if I fix any number among them as ghost and the measure all of majesty for which launches its have bigger than the Times was 1 of the area but tends to the OK so this the appearance assets as it stands is appearing for fixed values are of and as the ghost of when you can you can make it fall in incident but due to gain some insight let's assume that this this kind of behavior persists for all values of for all this was follows the case with the bigger you 1 reason why it falls so Matsumoto something about maybe "quotation mark the large values and small values so you can imagine that the being very very small like that maybe going to minus infinity and in this case you shouldn't expect too much uniformity in with the like this country can hold because suppose you want to that this that you're making some claim about the frequency with which worries more about something like this 1 where would you can produce more voters of data you take is the only take small neighborhood under their own you'll get worse over the few take that you will produce more small values than would be predicted by some of so you should not so you should not use so within that range not true loss small news but maybe you can assume that that's a supports it's true for enlargement of data or maybe it's true an upper bound so that you can get a balanced on 1 side and normalizes slightly differently so let's say that I suppose we assume that the measure of the 2 With Zeta have society bigger than some number at the that behaves the roughly like responded about something like exposed minus the square but am being a little crude here this is exactly the same as thing bill that I wrote down except for the flight normalization I made it clear to the regional leaders of the times as part of the variance on you know this interview roughly like he might be squared with 2 not exactly but roughly the same as it was good and that's what I have written down here again if you take into account the suppose that something like this sir so if you know that you can immediately get enough money for more so this will imply about from moment quite easily because what that took a moment of of 1 the values on which this is larger than somebody that we find measure of the facts on which takes values that are as so this will be the integral from mines and the utility of the times the change in the measure of such large which you can integrate but parts to To be able to use the power of the essentially the same as all maybe Rabin with a minor but because this is decreasing function so well that you did it apart to get up to minus signs which cancel so amount suppose you have a uniform upper bound for the measure on which Was can be hard you would get bounded by and you can just focus on what what is the range of values of wheat on which this is as large as possible that's a simple calculus exercise and you can see that this is maximized when you when to be case and for this value for all we know
that this integral is itself outside the law the where so you know it's not want that to get moment of the speaking of this to took a moment is really picking up the values of the offside locked into the into on the set of values of data on size of the team to the conducted became the center has measure which is about the only locked into the case so therefore if you take that to the moment of of this you get locked into the 2 cases where times the measure which is probably 1 or 2 which is like so you can see that there is this kind of an intimate connection between still looks the on on the value distribution of the aid of have slightly and the moment so you but the economics of the Keating state conducted what would be the analog of some conjecture on the value distribution of all the love and support functions which would produce producers and exporters of farm gate landscape of to work landscape get and these are just due to the marketing inside convictions of 2 to take that support would take although El kind and the variable fundamentals components state the 2 sides and we want to know the distribution of you can see that this is already a a more subtle problem then somebody for this because was OK I at blogs they don't have Poseidon it could be that they don't have society's What is the only authentic measures measures so I can ignore that and any statistical calculation that I but if you have a problem because if I look at a local have end have pretty happens to be the world's very often then I don't get a distribution of I can't ignore these these values but we knew conjecture that there are very few values so far of all the which I have ideas is the if I pretended to that their mobile of the for which any failed function vanish this is never expected to be 0 but if it is a role for a long time and we have a problem OK so to you can't we can't prove that this number 0 or 0 per set of density 1 so that's 1 reason why these Hamilton opulence but just conjecture but look at the now quite nice this is approximately normal but now there's a slight difference with names about since I the mean being the means about how long and the variance with larger for it's a wise the variance larger will there is a lot of they'd have society has a real problem in Nigeria on both can be baked and therefore usual the becomes you size of the 1 always square to salute square them and then they contribute 50 50 but this guy is always going to be a real number so therefore you get this variance being slightly larger I'll explain the meaning In just and similarly 1 can connect if you look at the logbook I'll have said it takes a model farm and I form on the canal have to submit so here we should be careful not to look at the overall but maybe with the fundamentalist commands to act for which the sign of the functional aggression is positive it's a sign of things to these values are also hurled them and there's no more to be said then I also alters a conviction that this is approximately With me my my times log and so and then I I what I want to say is that if you do the analog of the calculation that for the for the functions the took a moment in the trial of these families and reunite them in terms of value being offset size on the news these 2 conjecture you will produce exactly the exponents gave escapist 1 or 2 in the syntactic case of torque a different and Cape Times came as 1 of the 2 and you can kind of see the difference coming in in the means which is start small in 1 case wanting the name of negative the direction where the powers of the little moments of a smaller Katyn came minus 1 or 2 and large the India so let me give you the kind of a heuristic explanation for where the central appear come from the state some recent results on on the subprime loans for so let's so maybe to start with you can think of logs laid off after psyche you go you can moralist think of this as the sum of all kinds of money really helpful like of course income but it's not it's not very far from the truth if you can get that some at the height of the the it's kind of roughly very good approximation of maybe we can get some that exists on the power of the world break and then this is usually a good approximation 2 I think this is not completely clear but it's real let's pretend that something like this system but this is not complete because people 1 more easily if you take although was a function it's not just the some all kinds of some or all the kind powers with the formal work gave Peter so we have to worry about that the plains where the kind you don't the prime accusing the prime the fault at all the relevant because they're confident the facilities when I'm
context and what I have said that if some uniform emotional these conjectures was true then you would get compliments of the right order of magnitude 4 moments in these in these various examples so let me and my but some results from on upper bound which only described tomorrow so 1st there so the principle of law bonds was that if you can evaluate some plus a little bit then you can get more for all the all the higher moments so that a complementary principles which madam I have been working on recently Is that fair so instead of roughly as if you know some moment of steps along again the current alone the illustrate this by wealthier that in the in the context of of a model form or not to come to you hear the only moment that we know how to calculate is the 1st this been asymptotic sport and it's only moment that's the unconditionally and so what work is that it from 1 can prove you get the right of all apart from that we have a pretty good
Parametersystem
Lineares Funktional
Momentenproblem
Gruppenoperation
Zahlenbereich
Bilinearform
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Computeranimation
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p-Block
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