On multiple zeta values of level two
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 ... WebIn this paper, we define and study a variant of multiple zeta values (MZVs) of level two, called multiple mixed values or multiple M-values (MMVs), which forms a subspace of the space of alternating MZVs. This variant includes both Hoffman’s multiple t-values and Kaneko–Tsumura’s multiple T-values as special cases.
On multiple zeta values of level two
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Web19 de nov. de 2024 · We first review our previous works of Arakawa and the authors on two, closely related single-variable zeta functions. Their special values at positive and … Web31 de jan. de 2013 · Double zeta values are a special case of multiple zeta values, de ned by sums like (1) but with longer decreasing sequences of integers, which are known to …
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 … Web1 de jan. de 2013 · Introduction and main results Double zeta values of level 2 are deï¬ ned by ζ o(r, s)= ∑ 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 …
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 … 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 …
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
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 farmers almanac first freezeWeb10 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. … farmers almanac first frost date 2022Web7 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. farmers almanac first yearWeb2 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 … farmers almanac first frost 2022WebWe 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 … farmers almanac first frostWeb1.2. 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 … farmers almanac fishing 2023Webinteresting 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 ... free online reader books