Non-vanishing of multiple zeta values for higher genus curves over finite fields

2023/05/25 by Daichi Matsuzuki, Matsuzuki, Daichi
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2305.16218

openalex publication_date 2023/05/25 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that ∞-adic multiple zeta values associated to the function field of an algebraic curve of higher genus over a finite field are not zero, under certain assumption on the gap sequence associated to the rational point ∞ on the given curve. Using arguments and results of Sheats and Thakur for the case of the projective line, we calculate the absolute values of power sums in the series defining multiple zeta values, and show that the calculation implies the non-vanishing result.

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