On the linear relations among parametrized multiple series

2021/11/25 by Minoru Hirose, Hideki Murahara, Hirose, Minoru +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11M32

paper · pdf · doi:10.48550/arxiv.2111.12975

openalex publication_date 2021/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Parametrized multiple series are generalizations of the multiple zeta values introduced by Igarashi. In this work, we completely determine all the linear relations among these parameterized multiple series. Specifically, we prove the following two statements: the linear part of the Kawashima relation for multiple zeta values can be generalized to the parametrized multiple series; any linear relations among the parametrized multiple series can be written as a linear combination of the linear part of the Kawashima relation.

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