On the distribution of αp² modulo one over primes of the form [n^c]

2025/04/30 by S. I. Dimitrov, Dimitrov, S. I., M. D. Lazarova +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.21333

openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Let [ ⋅ ] be the floor function and ‖x‖ denote the distance from x to the nearest integer. In this paper we show that whenever α is irrational and β is real then for any fixed (13)/(14)<γ<1, there exist infinitely many prime numbers p satisfying the inequality ‖αp²+β‖lt; p^{(13-14γ)/(29)+ε} and such that p=[n^1/γ].

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