Zero Distribution of v-adic Multiple Zeta Values over \mathbbF_q(t)

2019/12/22 by Qibin Shen, Shen, Qibin
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1912.10365

openalex publication_date 2019/12/22 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

This paper aims to study the zero distribution of v-adic multiple zeta values over function fields. We show that the interpolated v-adic MZVs at negative integers only vanish at what we call the ''trivial zeros'', for degree one prime over rational function fields. And we conjecture that this result can be generalized to all primes.

Related

• Universal \mathbbF_q-Family of v-adic Multiple Zeta Values over Function Fields
• Integrality of v-adic multiple zeta values
• Algebra structure of multiple zeta values in positive characteristic
• Vanishing of Multiple Zeta Values over \mathbbF_q[t] at Negative Integers
• Distribution of Values of Real Quadratic Zeta Functions