Statistics of Different Reduction Types of Fermat Curves

TL;DR

This paper investigates the distribution of reduction types in Fermat curves, providing theoretical bounds and algorithms to analyze their statistical properties across various reduction scenarios.

Contribution

It introduces new theoretical bounds and algorithms for studying the reduction types of Fermat curves, advancing understanding of their statistical behavior.

Findings

Derived bounds on reduction type distributions

Developed algorithms for analyzing Fermat curve reductions

Enhanced understanding of Fermat curve reduction statistics

Abstract

We present some theoretic bounds and algorithms concerning the statistics of different reduction types in the family of Fermat curves $Y^p = X^s(1-X)$, where $p$ is prime and $s =1, ..., p-2$.