Group automorphisms with prescribed growth of periodic points, and small primes in arithmetic progressions in intervals

TL;DR

This paper explores the possible growth rates of periodic points in compact group automorphisms and employs a modified version of Linnik's Theorem to analyze small primes in arithmetic progressions within intervals.

Contribution

It introduces a novel approach combining automorphism growth analysis with a modified Linnik's Theorem to study prime distributions in specific intervals.

Findings

Characterization of growth rates for periodic points

Development of a modified Linnik's Theorem for intervals

Insights into prime distribution in arithmetic progressions

Abstract

We investigate the question of which growth rates are possible for the number of periodic points of a compact group automorphism. Our arguments involve a modification of Linnik's Theorem, concerning small prime numbers in arithmetic progressions which lie in intervals.