On multiple zeta values of level two

Author: itnv

August undefined, 2024

Web1 de dez. de 2024 · On multiple zeta values of level two. We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta … WebWe study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle counterpart' of Hoffman's `odd variant', exhibits nice properties such as duality, shuffle product, parity results, etc., like ordinary multiple zeta values. We also give some …

Double zeta values, double Eisenstein series, and modular forms of level 2

Web1.2. Multiple zeta values. Now consider the product of two zeta values, (k) (l) = X m;n>0 1 mknl: Splitting the domain into three parts, Euler observed that (k) (l) = X m>n>0 + X … WebThe multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators V1=−Δ+V1 and V2=−Δ+V2, with V1, V2 constant, in a D-dimensional compact smooth manifold MD, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the … ipsut creek

Evaluation of the multiple zeta values $\zeta(2,\dots,2,3,2,\dots,2 ...

Web7 de mai. de 2024 · D. Ma, Period polynomial relations between formal double zeta values of odd weight, Mathematische Annalen 365 (2016), 345–362. Article MathSciNet Google … WebWe study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle … Web9 de mar. de 2024 · We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is … orchard house wadebridge

[2109.01699] Valeurs zêta multiples - arXiv.org

Mixed Tate motives over Z - Annals of Mathematics

WebAbstract. We prove that any multiple t-value of maximal height (that is, all components of the index are greater than 1) can be written as a rational linear combination of multiple … Webmultiple zeta values of maximal height. 2010 Mathematics subject classiﬁcation: primary 11M32; secondary 11M41. Keywords and phrases: multiple zeta values, Arakawa–Kaneko zeta function. 1.Main results The multiple zeta value (MZV) is a real number given by the nested series (k 1;:::;k r) = X 0 ipsw a1687Web30 de nov. de 2024 · We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is … orchard house victoria bc

"WebWhen all of the are n th roots of unity and the are all nonnegative integers, the values of the multiple polylogarithm are called colored multiple zeta values of level. In particular, when n = 2 {\displaystyle n=2} , they are called Euler sums or alternating multiple zeta values , and when n = 1 {\displaystyle n=1} they are simply called multiple zeta values. " - On multiple zeta values of level two

On multiple zeta values of level two

Web7 de mai. de 2024 · The second author wishes to express his thanks to Herbert Gangl for drawing his attention to Yamamoto’s {1 \over 2} -interpolated multiple zeta values. The second author also thanks Max Planck Institute for Mathematics, where the paper was written, for the invitation and hospitality. Web26 de dez. de 2016 · It is more generally believed that all algebraic relations between multiple zeta values are implied by the (regularized) double shuffle equations, which are a class of quadratic relations between multiple zeta values. Specialized to the depth two case, they read

Did you know?

Web10 de ago. de 2024 · M. Kaneko and H. Tsumura, Zeta functions connecting multiple zeta values and poly-Bernoulli numbers, Adv. Stud. Pure Math. 84, 2024, pp. 181-204. … Weba level 2 multiple zeta value because of the congruence condition in the summation and of the (easily proved) fact that this value can be written as a linear combination of …

WebFor k ≤ n, let E ( 2 n, k) be the sum of all multiple zeta values with even arguments whose weight is 2 n and whose depth is k. Of course E ( 2 n, 1) is the value ζ ( 2 n) of the Riemann zeta function at 2 n, and it is well known that E ( 2 n, 2) = 3 4 ζ ( 2 n). Recently Shen and Cai gave formulas for E ( 2 n, 3) and E ( 2 n, 4) in terms of ... http://javier.fresan.perso.math.cnrs.fr/mzv.pdf

Web1 de mar. de 2012 · A formula is given for the special multiple zeta values occurring in the title as rational linear combinations of products ζ ( m) π 2 n with m odd. The existence of … WebEvery multiple zeta value (1:1) is a Q-linear combination of (1.2) f (n 1;:::;n r); where n 1;:::;n r2f2;3gg: In this paper we proveConjectures 1and 2using motivic multiple zeta values. These are elements in a certain graded comodule HMT+over the a ne ring of functions on the prounipotent part of G

Web1 de jan. de 2013 · Introduction and main results Double zeta values of level 2 are deï¬ ned by Î¶ o(r, s)= âˆ‘ m>n>0 m,n:odd 1 mrns , (1) here r, s are positive integers with r 2. …

Web2 M. RAM MURTY AND KANEENIKA SINHA This Hurwitz zeta function, originally deﬁned for Re(s) > 1, can also be ex-tended analytically for all s ∈ C, apart from s =1, where it has a simple pole with residue 1. In his study of ζ(s;x), Hurwitz was motivated by the problem of analytic continution of Dirichlet L-functions.For any Dirichlet character χ (mod q), we may … ipsw 6s+WebMultiple zeta functions are known to satisfy what is known as MZV duality, the simplest case of which is the famous identity of Euler : where Hn are the harmonic numbers . Special values of double zeta functions, with s > 0 and even, t > 1 and odd, but s + t = 2 N +1 (taking if necessary ζ (0) = 0): [4] ipsw a2602Webinteresting part is about multiple zeta and alternating multiple zeta values, so I will establish notation for them rst. For positive integers i 1;:::; k with 1 >1, the corresponding multiple zeta value is the real number (i 1;i 2;:::;i k) = X n1>n2> >n k 1 1 ni1 1 n i2 2 n i k k: This can be generalized to alternating multiple zeta values with ... orchard house westmancoteWeb17 de abr. de 2024 · We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is … ipsw a1688WebJavier Fresán ipsw a1524WebWe will mainly deal with three types of objects: Multiple zeta values (real numbers), modular forms (holomorphic func- tions in the complex upper half plane) and q-analogues of multiple zeta values (q-series with rational coe cients). ipsw activation lockWeb3 de set. de 2024 · We give a gentle introduction to the study of multiple zeta values, from Euler's solution to the Basel problem to modern Galois theoretic tools. We emphasize the … orchard house west hoathly