On multiple zeta values of level two

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August undefined, 2024

WebON MULTIPLE ZETA VALUES OF LEVEL TWO MASANOBU KANEKO AND HIROFUMI TSUMURA Abstract. We study a variant of multiple zeta values of level 2, which forms … Web23 de dez. de 2011 · Regularized motivic multiple zeta values are very natural generalization of usual motivic multiple zeta values and used in various situations 1 , however, there seems to be no work on their ...

ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT - Cambridge

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. These real values can be regarded as a kind of Euler ms (see Section 2) or multiple Hurwitz series (see [8]), which are well studied, but apparently it believed that the form … 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 ... chiltern lamb

On a variant of multiple zeta values of level two – arXiv Vanity

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. 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 … chiltern la

On a variant of multiple zeta values of level two - NASA/ADS

Multiple $L$-values of level four, poly-Euler numbers, and related …

WebWe 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). 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 … chiltern ladies hockey clubWebMultiple 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] chiltern larder cupboard

"Web1 de ago. de 2024 · Finite colored multiple zeta values We recall that finite MZVs and finite Euler sums are elements of the Q -ring A: = ∏ p ∈ P F p / ⨁ p ∈ P F p. Note that for N = 1, 2, the set A can be identified with A ( N) since all primes greater than 2 are odd and we can safely disregard the prime p = 2. In the rest of this section, we assume N = 3, 4 or 6. " - On multiple zeta values of level two

On multiple zeta values of level two

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. … 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

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Web3 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 … Web2. Open-string tree-level amplitudes Open-string amplitudes at tree-level are obtained from correlators on a genus-zero Riemann ... 1gexclusively, which in turn can be cast into multiple zeta values using eq. (2.5). As an example, the string correction to the ﬁve-point amplitude2 for the trivial permutation reads F23 =1 z(2)(s 12s 23 +s 12s ...

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 … 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 …

http://www-personal.umich.edu/~francc/files/zeta_talk.pdf Web31 de jan. de 2013 · For multiple zeta values, ζ (a, b) is expressible in terms of ordinary zeta values ζ (n) when a + b is odd. ... ... (unlike Eq. (10), this formula requires p to be odd). Eq. (11) was...

Web17 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 …

http://javier.fresan.perso.math.cnrs.fr/mzv.pdf grade 6 worksheets on circlesWeb1.2. 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 … chiltern league chessWebEvery 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 chiltern league cWeb26 de set. de 2024 · In this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences $(\{1\}^a,c,\{1\}^b),$ … grade 70 chain 3/8Web1.2. 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 n>m>0 + X m=n>0! 1 mknl: If one now takes products of zeta values with the above kind of double sums, one obtains triple sums of a similar shape. Iterating this ... chiltern law solicitorsWeb9 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 … grade 70 chain hardnessWeb26 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 chiltern landscape character assessment