On relations for the multiple q-zeta values
نویسندگان
چکیده
منابع مشابه
Multiple q-zeta values
We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...
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Abstract. Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q → 1. Here, we discuss the sum formula for multiple q-zeta values, and provide a self-contained proof. As a consequence, we also derive a q-analog of Euler’s ...
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Recently, Masanobu Kaneko introduced a conjecture on an extension of the derivation relations for multiple zeta values. The aim of this paper is to give a proof of the conjecture by reducing it to a class of relations for multiple zeta values studied by Kawashima. Also we will give some algebraic aspects of the extended derivation operator ∂ (c) n on Q〈x, y〉, which was defined by modeling a Hop...
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The generating function of the sums of multiple q-zeta values with fixed weights, depths and 1-heights, 2-heights, . . . , r-heights is represented in terms of specializations of basic hypergeometric functions.
متن کاملRenormalization of Multiple q-Zeta Values
Abstract. In this paper we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq(s1, . . . , sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang [12] on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process pr...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2007
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-007-9053-5