Identities for the Multiple Zeta (Star) Values
نویسندگان
چکیده
منابع مشابه
Algorithms for Some Euler-Type Identities for Multiple Zeta Values
. . . , s k are positive integers with s 1 > 1. For k ≤ n, let E(2n, k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n, 2) = 3ζ(2n)/4was extended to E(2n, 3) and E(2n, 4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n, k) and then ...
متن کاملPartition Identities for the Multiple Zeta Function
We define a class of expressions for the multiple zeta function, and show how to determine whether an expression in the class vanishes identically. The class of such identities, which we call partition identities, is shown to coincide with the class of identities that can be derived as a consequence of the stuffle multiplication rule for multiple zeta values.
متن کاملOn some explicit evaluations of multiple zeta-star values
In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of π. 1 Main Results The multiple zeta value (MZV) is defined by the convergent series ζ(k1, k2, . . . , kn) := ∑ m1>m2>···>mn>0 1 m1 1 m k2 2 · · ·m kn n , where k1, k2, . . . , kn are positive integers and k1 ≥ 2. The integers k = k1+k2+ · · ·+kn and n are called weight and dept...
متن کاملAspectsof Multiple Zeta Values
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuue product rule allows the possibility of a combi-natorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with ...
متن کاملMultiple Zeta Values
for any collection of positive integers s1, s2, . . . , sl. By definition, Lis(1) = ζ(s), s ∈ Z, s1 ≥ 2, s2 ≥ 1, . . . , sl ≥ 1. (4.2) Taking, as before for multiple zeta values, Lixs(z) := Lis(z), Li1(z) := 1, (4.3) let us extend action of the map Li : w 7→ Liw(z) by linearity on the graded algebra H (not H, since multi-indices are coded by words in H). Lemma 4.1. Let w ∈ H be an arbitrary non...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2018
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-018-0761-5