On Multiple zeta values and their qanalogues
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On Multiple zeta values and their qanalogues

Alternative Title 
HopfAlgebraic Renormalization of Multiple Zeta Values and their qanalogues

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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. 
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2021

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English

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Abstract 
After a brief introductory account, I’ll explain how a quasishuffle compatible definition (by no means unique) of multiple zeta values can be given for integer arguments of any sign, through ConnesKreimer’s Hopfalgebraic renormalization. Finally, I’ll introduce the OhnoOkudaZudilin model of qanalogues for multiple zeta values, describe the algebraic structure which governs it, and explain how it could open a way to the more delicate renormalization of shuffle relations.

00:00
INTEGRAL
Weight
Multiplication sign
Mathematical singularity
Kontraktion <Mathematik>
Parameter (computer programming)
Mereology
Grothendieck topology
Variable (mathematics)
Group representation
Coefficient of determination
Roundness (object)
Different (Kate Ryan album)
Bernoulli number
Extension (kinesiology)
Position operator
Theory of relativity
Sigmaalgebra
Moment (mathematics)
Complex (psychology)
Maxima and minima
Perturbation theory
Price index
Term (mathematics)
Time domain
19 (number)
Hand fan
Series (mathematics)
Number theory
Theorem
Relation <Mathematik>
Summierbarkeit
Spacetime
Functional (mathematics)
Rule of inference
Product (business)
Time domain
Gezeitenkraft
Causality
Modulform
Homomorphismus
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Multiplication
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Quantum state
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Weight
Gender
Skewness
Volume (thermodynamics)
Numerical analysis
Voting
Function (mathematics)
Factory (trading post)
Network topology
Object (grammar)
Musical ensemble
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08:01
Commutative property
Complex (psychology)
Presentation of a group
Open set
Variable (mathematics)
Explosion
Group representation
Roundness (object)
Different (Kate Ryan album)
Isomorphieklasse
Forest
Bernoulli number
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Pole (complex analysis)
Proof theory
Potenz <Mathematik>
Theory of relativity
Infinity
Meromorphe Funktion
Product (business)
Hand fan
Duality (mathematics)
Helmholtz decomposition
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Theorem
Analytic continuation
Point (geometry)
Slide rule
Twin prime
Sine
Diagonal
Similarity (geometry)
Drop (liquid)
Infinity
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Morphismus
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Complex number
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Modulform
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Newton's law of universal gravitation
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1 (number)
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Iterated function system
Parameter (computer programming)
Mereology
Hopf algebra
Duality (mathematics)
Cuboid
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Logarithm
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Polylogarithmische Funktion
Physicalism
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Proof theory
Isomorphieklasse
Pareto distribution
Right angle
Pole (complex analysis)
Resultant
Blind spot (vehicle)
Differenz <Mathematik>
2 (number)
Local Group
Mach's principle
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Gezeitenkraft
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Homomorphismus
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24:02
Commutative property
Convolution
Group action
Beta function
Multiplication sign
Correspondence (mathematics)
Mathematical singularity
Kontraktion <Mathematik>
Parameter (computer programming)
Mereology
Cuboid
Renormalization
Recursion
Pole (complex analysis)
Position operator
Proof theory
Propositional formula
Maxima and minima
Hopf algebra
Statistics
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Hand fan
Category of being
Proof theory
Phase transition
Order (biology)
Mathematical singularity
Theorem
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Ideal (ethics)
Analytic continuation
Electric current
Spacetime
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Functional (mathematics)
Maxima and minima
Differenz <Mathematik>
Axonometric projection
Subgroup
Event horizon
Theory
2 (number)
Product (business)
Local Group
Prime ideal
Goodness of fit
Network topology
Profil (magazine)
Wellformed formula
Modulform
Spacetime
Analytic continuation
Maß <Mathematik>
Alpha (investment)
Condition number
Metre
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Weight
Expression
Projective plane
Line (geometry)
Mortality rate
Group action
Limit (category theory)
Numerical analysis
Kontraktion <Mathematik>
General relativity
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Function (mathematics)
Musical ensemble
Maß <Mathematik>
32:27
Commutative property
Complex (psychology)
Model theory
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Divisor (algebraic geometry)
Open set
Johann Peter Hebel
Estimator
Negative number
Hill differential equation
Multiplication
Descriptive statistics
Regulator gene
Infinity
Parameter (computer programming)
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Hand fan
Series (mathematics)
Duality (mathematics)
Number theory
Relation <Mathematik>
Summierbarkeit
Spacetime
Sine
Beat (acoustics)
Endomorphismenmonoid
Maxima and minima
Drop (liquid)
Regular graph
Shift operator
Product (business)
Term (mathematics)
Associative property
Maß <Mathematik>
Matching (graph theory)
Quantum state
Uniqueness quantification
Weight
Classical physics
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Operator (mathematics)
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Basis <Mathematik>
Line (geometry)
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Mathematics
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Finite difference
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Integer
Building
INTEGRAL
Weight
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Parameter (computer programming)
Food energy
Grothendieck topology
Thomas Kuhn
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Series (mathematics)
Algebra
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Algebraic number
Moment (mathematics)
Complex (psychology)
Inverse element
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19 (number)
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48:43
Axiom of choice
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Summierbarkeit
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00:01
[Music] 5 very much to touzet organizer are special two g?rard fordisme nice invitation au ici des six de la space au to jump to the beginning sorry for de hockey here we go so i also where they steal votes multiples and to his 5 stones in stock and will go slightly quickr on ging his azioune with multiple zetas are 10 intelligence among the trees that they were you sting your multiples the state will use the enjoys art positivity joss a divine if i want serristes converge yoni from anyone bigger than two hockey you can't go slightly behind you could go to enjoy positive in negative bots you must have in one place and it's all strict angie bigger than just for any jet from one touquet which are to what one aux in tedjar that is 22 some of the unjust is the weight hockey are just let me but this moment their historical watch beef at amina customs ouch start with other in eighteenth century news multiples and as in depth one two three guys lot of relations '' between them not all we know are are at lot they swap now back up to life inc fifteen years ago only once we win win your game ready for your hands and the big gap tonnetil nineteen eighties drop 10 gap is not completely a little big boss for example mines indicating that you can't find some example elsewhere in aix in the work of nilsen begging of the last century entre vennes up to my knowledge multiples and years the worst first at the ruling see that fleury callune nineteen and iwan the functions resurgent volume of hockey so what about multiple state works not thus argued even complex balls there are two thresholds we are except do you have jace complex art our indian customs hylton 100 dates here semitrailers sync function is variable this is the world as we japanese researchers akiyama et gamines tanigawa of a convergys provided service is restarted because we are strict and virginie jay and you can extent mermozmarty parcels to school site the key oui ce vari?ty of things like this which is described as follows [Music] in depth key of singles in the heart of cairo he says he is fine dallas paulos des cistes jose they thought that is her z one big one to one or ziouane poetry to belong to set your form to buy all accept everything at zero and or their exist forms touitou key only date 10 by only thing here under this word their Shoulders everything so I s all you can see the difference between the one to one ce we however underline that the date single the state works a can be contes inuit analytical evolve with 70 one out for dobles and his ten roses come from the fact date bernoulli numbers de haute bernoulli numbers hall vanish accept the first one ok its island describe the bulge fabrication what causes we will see generalization jo frost who did not dare to product of two single zetas is some of sweet home stuber et ? saintes de diagonale tort witches guen singles to states and profit forces this laughter you you get the domain d'oussouye parts and  bigger than two monines smaller than two testify all and all things thompson diagonal but worse ok with a describe moss general 3 eichhoffen relations are safe it multiplies all multiple states either 9 of eps pee or a hot dog skew eynden you get some after death of death pipe lost you mind of something is something is more is the number of contraction will finish tome en tome factory dext overall to cross eichhoffen the pitch your mother of all the time of oak is a teaser on six sigma from one up to be lost you want to one up to pick losc human us size aps object hussein relations '' once in shooter mind of earth too thin and cool to something of the second round of a fabric to the contractions jones draws from the arguments cindy contracts from multiple and to different people the sums proud indices sums if you think about it he counted there are one but beetroots your hockey notebook are probably the only one with integrals representation of multiple offers the state value August 10 where maxim concewitz enters coded bae dont zag and a ninety nine tifo oil crisis to which are multiples and downstream you here now enjoy his gender positivity he says he is not a fan hysteria full tease is 8 and rhythm to this match at the wait until you going green tic integrated iphone only form stiti opportunity over you want
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miles austin lynch has wrong to offer it you have and thorns soul to gather after that you have and soul to gather in den pierre engels all together graff different shapes stiti with nettles except last of the pack is here said yu hwan dynasty of caunes six points on the second round on purpose of product of two multiples and its line to combine shirt with heating collar relation for example to hits multiple assets akbar hesitate at all it is quadruple integral with different wines only forms a small integrate overs product of two simply 6 1/10 product of two simply 6/10 cintu compound 6 strong dimensional simply 6,1 des nuggets x top four times and in taiwan place to time and aof still ok to regularize elections amorfini the simplest one is the world in home builders and house to one is equal to et ? autrui et need you now one ok you will say to me that of one's own exists ok this is just owning determines is still seen in stock samara au yukon decided that of magical zero rate baptized the stone age and ermine is an if your idols and before all in the united states singh starting with you want is also elsewhere jones sono to wilrijk in ten product in two different ways open jaws by formulated using to cross eichhoffen relations and the bottom line is just for money by using chauffeur relations and then i fiul if you equest or even bros the red tails disappear like in clinical reaction a tube get en france this one 10 th coin il a toi nantes you get the wailers collection and of physical everything is off to one to which are briefed explain the bird driver relationship dope the driver fat regularization haunting driver to adapt our soccer relationship for example raf must tell him things like a form of chengdu variable the dj ikk aux to one man city james ellroy presentation ban ahly pull the pampers by des idioties boys from the bulge for example 10,6 de faire ce exemple of duality ans you have we said as we have seen on the balshaw jump end a goal you have valve springs and the relationships that exist between principle to be explosives bat as far as they know it's still duality religion as from beautiful things ok there is hockey are multiple politocards considers justin wang variable her face already explodes her rudder clichy multiple paulilles to the boys at some type twin 0 in one he says to himself fan base are there on x different bases disintegration s25 multiple forms and enough that this date instead of going for zero to one you stop and i want someone is the world he wants multiple levels and downstream you would be divergent and stop at his strictly smaller than one he distils like georges issiot to whom his name and one two weeks press 10 multiple poles he parked his hymn to operators yeah ok 066 de formula you can't think the bottom of the slide on you start with the coast depending on the cultures and you lie and operators big one which is multiplied by malfunctions one over one man city ok wine reply from operators arts a witch's by primitive operators parents would have made physical to the primitive of f vanishing and 0 10 and 0 tobacco stop inheriting to the box in vein and we continue or like this you play non operator x86 bits multiply multiply bailly molex and six officials one oberti eynden operative etc etc over 800 dancers way to two two rewrite concewitz integrale performance 9 multiple polished logs hockey unless our want is called to one you will cover the multiple stages at the wimax checkouts ten representations by words yoyo introduce infinite alphabet alphabets why why star of this of words twitter chinese look at the line up and of the world un pipe k23 eichhoffen produces his bail point of view there are at hodiall to the wall explained bailly mines instead of using concatenation products dijon fco product will use de quazal shuffle product in conquests and nations co productive there ok it's up to crises to cross eichhoffen product so it's like that he was eichhoffen relation where we are poor from sat 3:22 pm rue sipilou xv th ri similar serious contraction of eleven countries that we say ah ok except or later use one gets worse define disc white pearl project kahn stick to jean winshuttle to min ? cannes stick to war equal to zero so high tech smaller are one of the few sodi fine associatif product which is no ordinary only product bastille landis infinite alphabets are taken as an example three eichhoffen hirai a life turns including by this to contraction term ce bati fault 10 cardiac driver product at the crates bone 10 6 3 10 a white star annotation managed account jones j call to this time switch d'hondt start with my
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one and for any world for any converging world with andy fiennes and aquoise eichhoffen of the world is equal toulouse et tarbes the corresponding europhile 10 battle afghan risk of attack that annick stand in early between de quazal chauffeur relation with who wants to the fact that they state it is to cross eichhoffen in the character do fort de quazal surfer product is morphism of course we would like to go from counter jones world to a newer de that's what i mean explained hao tour et gueulard eyes the world switch arnott convergent which are six young people example we cross reformulation written in terms of the coast choppers product with 1go duvet whatever we say ok sound haiti from first ryzolt eyes open with sylvie fishermen are scabbard hugo boots extentions all argument except and nice i'm ok said because of quazal surfers pro doc to you can extended to the world slater seen in if hockey his camping form strong argument except positive out negative sign hockey on what will prove ii x2 following their this character form 10 extended algebra with the crash of product in tour de complexes moeurs so that just to the mad fayos life easyquote to the external states fit for any convergent world ok it's when you read strong uni world with the positive negative letter only that the multiple and to can be defined by analytic continues and shenzhen the character that a series of 8.6 analytical y extended value are a particular firefly neeskens equal to and aof mindset his bernoulli lineup a place either new rules or are followers to fail of mind hossein mindset prime jcall toulouse and mainz germany this premium sauser this webmaster the value read ifs enterprise fraud clue that does not give and say expression in this fire bernoulli nos news so we got the wolf of value in depth all in any case except alioune il rises diagonale cyr have all the same value except the very last one and one note for example 10 one ok 10 value its obtained by analytical continuation diagonal rises ce are not only for example there will be walsall paper by the iguana bintang the little bee for us they also have tech of the value it offer is different boots of course 2 drops diagonal squeeze out because analytical continuation ok there you me guy basket of proof are they those who like kreiner regularization a renormalization vehicle ok this we have the right of oil products together with concatenation you get connected filter up jay bryson by the index of names xtend October 10 at 12 p.m. or letter sin of complex numbers sow extended match my style or quest for europe thrills its fans arms yes to cross eichhoffen product replaced by the chauffeur product hockey at the results paris michael hoffman 10 to have fun I brush orphic rhizome the tunes are explicit isomorphism victor mappy their regularization map so we said fanny tons of wood warms up a europe version algebra solidaire considers paul bigard of the world is the c word between 10.6 shifted bezina like this ok and then we will use dissent of man exponential luis witches from europe parisot mon physio eynden from the gold regularization in ayguette regularization bee artiles christine galzin hoffman exponential except twisted regularization respects corner ike pro surfers of anticosti first regularization houde respects driver product sino on three now yes says character fan big five from 10 and the browser for product design by this horgen zh and what to heat zamal kippel the state works it gives me back orfi which is not in complex variables they are by defeating this is it that it ex cintu value of mary murphy which works if one complex variable eynden then we have the birkhoff kreiner decomposition gold au big big fail character can be composing like this are a 6.2 convolution of product a tops if their style characters three axes a relation sarr style verified faille plus au viie solo morphy cadic wall to zero forest new world we want this is what we want it because non ok 10:10 hour of formulation gate 2 to peace is fine to the faults more of my agricultural goods quickly as it works your mirror fiq works algebra explains into parts of paul pierce and mind at Formalin breast sparta series and it cries ok so if socalled minimoys abstraction of skimming physics and then you can define recursive lifan magnussen flaw more 06/08/10 formula register the writer speech of bogoliubov
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preparation of maps and even if you ou tu exeo positive project in good for the party is sure that we find you projectim of formalin service parts which was to ana?s character and then de character we will look for you just evan lloyd de grosses parts said what the zero rate of 10 seconds or a style verify horse ok so we are quite shrinks ryzolt eynden few years after that we wanted with crochet brahimi fardin day one thing we wanted to describe olsen ocean of the problem is quite the set characters winch external multiple state functions if linda 100 Gbagbo respecting mines crossed against a background of relation normalizes this mesh sound band he has heavy rain say ok a tone is 7000 and mrsweets28 general ryzolt to sad stories commutative connected filter of europe angie brad i will be any commutative unit which jim brown jr will be the group's characters witz val using products given by the construction of disco ni potence property witch et disco soul to make some recursive hockey argument proposal of kids as follows ue arises date big ny will be there ideal tco where they respect each other or reduce the product reviews product is this delta tilda who stares form relaxation extract and / or extreme turns hockey and then it's you look at 17.6 hey you look at the characters alpha with the vanishing wright that elsewhere visiting this group from profits what quiksilver in the blind proves the sunlights or the world it was said was take two and the hands sales fans cattle ne t'y as you want to prove that alfabeta manos one i still in this way to prove it is this group titled you say that in there the characters event composition of the antipodes and yes yes place of a type to the hosts bdx recursive expression one of the nude can alphan manas beta of the boys or prime in cairo between new look of the youth of right right cori crider property to say that is vanishes hockey so we call it de renormalization associated groups all that it doesn?t like this district you look at work the different characters your mix it if i'm only and co hayden interview arises date is respected unit between x multiplicative whenever twitter define the sweetest belong to and not to loket ex et ? l'oeil easy call to those flaw underline two groups of seals almost restricted to indicate 12 states ok outdoor intelligence of the six main homogeneous and space yes yes poor straw and yes his left ibrahim sy lighthouse of the oan's ignore if this homogeneous principle and space administration crisis fringe positive in two squat profiles similar to the proof of being told i was group ok skip say ok no yes the dish it says gerald framework to our people zetas sobeys phillies from reading numbers of fate gibrat is this one with des arguments end i'm into you of total i embroider will be just complex our morals the white white world is the line hispanophone singer words that means that the world in which way down like this and switch poe le fil district conditions switch the contrarie of the singularity conditions except the beginning of the top weight and has to be different from one in one person to as to be outside 17 ans disparue le sol forgetfulness phase outside 17 hockey between ten times ok 10 big and so cute read aitzol ford concatenation mister k say yes we say choose six hours additional and pro ported on the stephen barry contraction this exists ok yungas men consecutive their health where we are and mup the slips and nice people by this properties which are sigma will biz complementary n hockey en sauce ig markets group that the corresponding mobile home staging du abb local what is a bit by that define characters and how will be at ok will be multiple state will user baikonur johnson in theory did are out of broom analytics continuation of sound hockey to this offers a solution while initiating the forum it given by the run ar re normalize groupe acti ngon one solution fortune holding as we had proved with sylvie p?cha that one 'solution' exists ok sowind vesti gay title little big disk group just to say that it's very big fuel audi has destroyed or also to this crazy lotto but to which his agent or cumana locks at the box let me in mind what is jackson integrale in the given by the ugly formula bat baby it's easy to grasp
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