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arXiv · 2404.01047

On the distribution of $\alpha p+\beta$ modulo one for primes of type $p=ar^2+1$

T. Todorova
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Abstract

A classical problem in analytic number theory is to study the distribution of fractional part $\alpha p+\beta$ modulo 1, where $\alpha$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p=ar^2+1$ and prove that its distribution has a similar property.

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T. Todorova. 2024-04-01. On the distribution of $\alpha p+\beta$ modulo one for primes of type $p=ar^2+1$. https://arxiv.org/abs/2404.01047

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