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 ... 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 …

Multiple zeta function - Wikipedia

WebUpdated Mars 2, 2024 MZV IMSc 2011 1.2 Multizeta values: Zagier’s conjecture The situation changes drastically if we enlarge our set so as to include the so-called Multiple Zeta Values (MZV, also called Polyzeta values, Euler-Zagier numbers or multiple harmonic series): (s 1;:::;s k) = X n 1>n 2> >n k 1 1 n s 1 1 nk k which are de ned for k ... Webinteresting 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 ... order form t shirt template free

[2109.01699] Valeurs zêta multiples - arXiv.org

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 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 ... 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 ... 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. … ireader pc端