Regular primes, non-Wieferich primes, and finite multiple zeta values of level $N$

TL;DR

This paper introduces finite multiple zeta values of arbitrary level and explores their connection to regular and non-Wieferich primes, proposing alternative approaches to longstanding prime infinitude problems.

Contribution

It extends the concept of finite multiple zeta values to general levels and links their properties to prime classification, offering new perspectives on prime-related conjectures.

Findings

Finite multiple zeta values of general level are introduced.

The relationship between these values and prime types is analyzed.

Proposed alternative problems related to prime infinitude.

Abstract

We introduce finite multiple zeta values of general level and discuss the relationship between the non-zeroness of these values and regular or non-Wieferich primes. Because it's challenging to prove the infinitude of these types of primes, we suggest tackling several related problems more promptly.