An alternate proof of idempotent relations among periodic points and\n quotients

2019/05/22 by Xander Faber, Faber, Xander, Michelle Manes +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1905.09378

openalex publication_date 2019/05/22 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

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

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