Sum formula for finite multiple zeta values
نویسندگان
چکیده
منابع مشابه
Weighted Sum Formula for Multiple Zeta Values
Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...
متن کاملON THE SUM FORMULA FOR MULTIPLE q-ZETA VALUES
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 ...
متن کاملSUM OF MULTIPLE q-ZETA VALUES
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 کاملON THE SUM FORMULA FOR THE q-ANALOGUE OF NON-STRICT MULTIPLE ZETA VALUES
In this article, the q-analogues of the linear relations of non-strict multiple zeta values called “the sum formula” and “the cyclic sum formula” are established.
متن کاملAn Algebraic Proof of Cyclic Sum Formula for Multiple Zeta Values
We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by reducing them to Kawashima relation.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2015
ISSN: 0025-5645
DOI: 10.2969/jmsj/06731069