# An alternate proof of idempotent relations among periodic points and quotients

## TL;DR

This paper presents a concise proof of an idempotent relation formula for counting periodic points of endomorphisms over finite fields, simplifying Walton's original approach by leveraging a theorem of Kani and Rosen.

## Contribution

It provides a direct proof of an existing formula, replacing formal manipulations with a more straightforward argument based on known theorems.

## Key findings

- Simplified proof of the idempotent relation formula
- Direct derivation from Kani and Rosen's theorem
- Enhanced understanding of periodic point counting

## Abstract

We give a short proof of an idempotent relation formula for counting periodic points of endomorphisms defined over finite fields. The original proof of this result, due to Walton, uses formal manipulation of arithmetic zeta functions, whereas we deduce the result directly from a related theorem of Kani and Rosen.