Zeta and L-functions

Multiple zeta function

In mathematics, the multiple zeta functions are generalisations of the Riemann zeta function, defined by and converge when Re(s1) + ... + Re(si) > i for all i. Like the Riemann zeta function, the multiple zeta functions can be analytically continued to be meromorphic functions (see, for example, Zhao (1999)). When s1, ..., sk are all positive integers (with s1 > 1) these sums are often called multiple zeta values (MZVs) or Euler sums. These values can also be regarded as special values of the multiple polylogarithms. The k in the above definition is named the "depth" of a MZV, and the n = s1 + ... + sk is known as the "weight". The standard shorthand for writing multiple zeta functions is to place repeating strings of the argument within braces and use a superscript to indicate the number of repetitions. For example, (Wikipedia).

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Multiple Zeta Values - Francis Brown

Francis Brown CNRS/Institut de Math. de Jussieu, Paris April 19, 2012 I will report on some recent work on multiple zeta values. I will sketch the definition of motivic multiple zeta values, which can be viewed as a prototype of a Galois theory for certain transcendental numbers, and then

From playlist Mathematics

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More identities involving the Riemann-Zeta function!

By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Riemann Zeta Function

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Some identities involving the Riemann-Zeta function.

After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Riemann Zeta Function

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More Riemann Zeta function identities!!

Building upon our previous video, we present three more Riemann zeta function identities. Video 1: https://youtu.be/2W2Ghi9idxM Video 2: https://www.youtube.com/watch?v=bRdGQKwusiE http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcollege.e

From playlist The Riemann Zeta Function

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Seidai Yasuda - Integrality of p-adic multiple zeta values...

Séminaire Paris Pékin Tokyo / Mercredi 8 avril 2015 Integrality of p-adic multiple zeta values and application to finite multiple zeta values Abstract : i will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upp

From playlist Conférences Paris Pékin Tokyo

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Monotonicity of the Riemann zeta function and related functions - P Zvengrowski [2012]

General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences May 17, 2012 14:00, St. Petersburg, POMI, room 311 (27 Fontanka) Monotonicity of the Riemann zeta function and related functions P. Zvengrowski University o

From playlist Number Theory

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Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 2.mov

More example problems involving the integral of 1 over u, du.

From playlist Transcendental Functions

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How to Evaluate a Multivariable Function Defined by an Integral

How to Evaluate a Multivariable Function Defined by an Integral If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)

From playlist Calculus 3

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Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 1.mov

Example problems involving the integral of u to the power negative 1 du.

From playlist Transcendental Functions

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Michael Hoffman: Multiple zeta values and alternating MZVs arising from a combinatorial problem

The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: Guy Louchard posed the problem of obtaining the general term of an asymptotic expansion of a certain definite integral. This led several peop

From playlist Workshop: "Periods and Regulators"

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David BROADHURST - Tasmanian Adventures

I report on two adventures with Dirk Kreimer in Tasmania, 25 years ago. One of these, concerning knots, is not even wrong. The other, concerning a conjectural 4-term relation, is either wrong or right. I suggest that younger colleagues have powerful tools that might be brought to bear on t

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

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Theory of numbers: Dirichlet series

This lecture is part of an online undergraduate course on the theory of numbers. We describe the correspondence between Dirichlet series and arithmetic functions, and work out the Dirichlet series of the arithmetic functions in the previous lecture. Correction: Dave Neary pointed out t

From playlist Theory of numbers

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CTNT 2018 - "L-functions and the Riemann Hypothesis" (Lecture 2) by Keith Conrad

This is lecture 2 of a mini-course on "L-functions and the Riemann Hypothesis", taught by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2018 - "L-functions and the Riemann Hypothesis" by Keith Conrad

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CTNT 2018 - "L-functions and the Riemann Hypothesis" (Lecture 3) by Keith Conrad

This is lecture 3 of a mini-course on "L-functions and the Riemann Hypothesis", taught by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2018 - "L-functions and the Riemann Hypothesis" by Keith Conrad

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Introduction to number theory lecture 45 Dirichlet series

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We introduce Dirichlet series as generating functions of arithmetical functions and give so

From playlist Introduction to number theory (Berkeley Math 115)

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Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3)

Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3) Licence: CC BY NC-ND 4.0Lecture I. I’ll give a complete elementary presentation of the essential features of the Perron Frobenius theory of nonnegative matrices for the central case of primitive matrices (the "Perr

From playlist École d’été 2013 - Théorie des nombres et dynamique

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Pierre Vanhove - Théorie des cordes et théorie des nombres : valeurs multiples zêta (...)

Dans ce cours nous présenterons les relations entre la théorie des nombres et les propriétés physiques des amplitudes. Nous présenterons la relation entre la condition d'univaluation des grandeurs physiques, et la notion introduite par Francis Brown. Nous discuterons le rôle de l'invarianc

From playlist 10e séminaire ITZYKSON – Valeurs zêta multiples et fonctions modulaires de graphes en théorie des cordes

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CTNT 2018 - "L-functions and the Riemann Hypothesis" (Lecture 1) by Keith Conrad

This is lecture 1 of a mini-course on "L-functions and the Riemann Hypothesis", taught by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2018 - "L-functions and the Riemann Hypothesis" by Keith Conrad

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Multivariable Calculus | A special double integral.

We describe a special case of a double integral over a rectangular region. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus | Multiple Integrals

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Michal Eckstein: Asymptotic and exact expansion of spectral action

The asymptotic expansion of the spectral action at large energies is powerful tool for building models of fundamental interactions. For a suitable almost-commutative geometry it encodes the full lagrangian of the Standard Model minimally coupled to gravity. However, beyond the almost-commu

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

Related pages

Journal of Number Theory | Analytic continuation | Shuffle algebra | Mathematics | Partition (number theory) | Harmonic number | Dirichlet eta function | Leonhard Euler | Riemann zeta function | Shintani zeta function | Meromorphic function