p-adic unit roots of L-functions over finite fields

TL;DR

This paper investigates p-adic unit roots and poles of L-functions associated with exponential sums over finite fields, exploring their quantity, congruence relations, and implications for arithmetic mirror symmetry.

Contribution

It introduces new insights into the behavior of p-adic unit roots of L-functions and their relation to arithmetic mirror symmetry.

Findings

Number of p-adic unit roots or poles analyzed.

Established congruence relations on units.

Raised questions connecting to arithmetic mirror symmetry.

Abstract

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a question in arithmetic mirror symmetry.