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arXiv · 2404.01045

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

T. L. Todorova
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Abstract

A classical problem in analytic number theory is to study the distribution of fractional part $αp^k+β,\,k\ge 1$ 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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T. L. Todorova. 2024-04-04. On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors. https://arxiv.org/abs/2404.01045

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