On the distribution of αp²+β modulo one for primes p such that p+2 has no more two prime divisors

2024/04/01 by Tatyana Todorova, Todorova, T. L.
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.01045

openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical problem in analytic number theory is to study the distribution of fractional part αp^k+β, k≥ 1 modulo 1, where α is irrational and p runs over the set of primes. For k=2 we consider the subsequence generated by the primes p such that p+2 is an almost-prime (the existence of infinitely many such p is another topical result in prime number theory) and prove that its distribution has a similar property.

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