Shuffle product of finite multiple polylogarithms

2015/02/24 by Masataka Ono, Shuji Yamamoto, Ono, Masataka +2
Mathematics · #11M32 #40B05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M32 #msc:40B05

paper · pdf · doi:10.48550/arxiv.1502.06693

13 pages

arxiv created 2015/02/24 · openalex publication_date 2015/02/24 · arxiv updated 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define a finite sum analogue of multiple polylogarithms inspired by the work of Kaneko and Zaiger and prove that they satisfy a certain analogue of the shuffle relation. Our result is obtained by using a certain partial fraction decomposition due to Komori-Matsumoto-Tsumura. As a corollary, we give an algebraic interpretation of our shuffle product.

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