t-adic symmetric multiple zeta values for indices with alternating 1 and 3, starting with 1 and ending with 3

2025/03/11 by Fujita, Kento
#11M32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.08380

Abstract

Hirose, Murahara, and Saito proved that some t-adic symmetric multiple zeta values, for indices in which 1 and 3 appear alternately in succession, can be expressed as polynomials in Riemann zeta values, and conjectured similar formulas. In this paper, we prove the conjectured formula for indices that start with 1 and end with 3, showing that they also can be expressed as polynomials in Riemann zeta values.

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