Combinatorial Aspects of Multiple Zeta Values
نویسندگان
چکیده
منابع مشابه
Combinatorial Aspects of 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 shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with...
متن کاملAlgebraic Aspects of Multiple Zeta Values
Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves “coding” the multiple zeta values by monomials in two noncommuting variables x and y. Multiple zeta values can then be thought of as defining a map ζ : H0 → R from a graded rational vector space H0 generated...
متن کاملA Combinatorial Identity of Multiple Zeta Values with Even Arguments
Let ζ(s1, s2, · · · , sk;α) be the multiple Hurwitz zeta function. Given two positive integers k and n with k 6 n, let E(2n, k;α) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. In this note we present some generating series for the numbers E(2n, k;α).
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: The Electronic Journal of Combinatorics
سال: 1998
ISSN: 1077-8926
DOI: 10.37236/1376