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A discretization of the iterated integral expression of the multiple polylogarithm

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arxiv 2404.15210 v1 pith:PQMTKMFT submitted 2024-04-23 math.NT

Minoru Hirose , Toshiki Matsusaka , Shin-ichiro Seki This is my paper · ORCID
classification math.NT
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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.

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  1. Truncated Hypergeometric Functions and Discretized Integrals

    math.NT 2025-07 accept novelty 5.0 of 10

    A new truncation of the hypergeometric series obeys an exact discretized-integral identity, and a finite analogue of the Ohno-Zagier formula is proved.

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