A discretization of the iterated integral expression of the multiple polylogarithm

2024/04/23 by Minoru Hirose, Hirose, Minoru, Toshiki Matsusaka +3 · 2 citations
Mathematics · #11M32 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.15210

openalex publication_date 2024/04/23 · openalex created_date 2024/04/26 · openalex updated_date 2026/07/28

Abstract

Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and provide two proofs. The first proof uses the method of connected sums, while the second employs induction based on the difference equations that discrete multiple polylogarithms satisfy. We also investigate several applications of our main result.

Cited by

• Truncated Hypergeometric Functions and Discretized Integrals
• The ℤ-module of multiple zeta values is generated by ones for indices without ones

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