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An interpolation of Bradley's sum formula

Anju Yokoi

Abstract

The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

An interpolation of Bradley's sum formula

Abstract

The sum formula for -multiple zeta values is a well-known relation. In this paper, we present its generalization for the -multiple zeta function.

Paper Structure

This paper contains 3 sections, 9 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['thm1']}
  3. Proof of Theorem \ref{['thm2']}

Key Result

Theorem 1.1

For integers $k$ and $r$ with $1\le r\le k-1$, set Then we have

Theorems & Definitions (21)

  • Theorem 1.1: Sum formula for qMZV; Bradley Dav
  • Theorem 1.2: Sum formula for MZF; Hirose--Murahara--Onozuka HMO
  • Theorem 1.3
  • Remark 1.4
  • Definition 1.5
  • Remark 1.6
  • Theorem 1.7
  • Remark 1.8
  • Lemma 2.1
  • proof : Proof of Theorem \ref{['thm1']} for $\sigma>2$.
  • ...and 11 more