PreprintCC BY 4.0HAL
On the distribution of αp³ modulo one over special primes
Abstract
Let [x] denote the integer part of x ∈ R, and let ∥x∥ denote the distance from x to the nearest integer. In this paper we prove that, whenever α is irrational number and β is any real number, then for any fixed \frac{47}{48}<γ <1, there exist infinitely many prime numbers p satisfying the inequality ∥αp^3 + β∥
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BibTeX
@misc{dimitrov2026distribution,
title = {{On the distribution of αp³ modulo one over special primes}},
author = {Stoyan Dimitrov and Meglena Lazarova},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05089082v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the distribution of αp³ modulo one over special primes
AU - Stoyan Dimitrov
AU - Meglena Lazarova
PY - 2026
DA - 2026/09/24
PB - HAL
UR - https://hal.science/hal-05089082v2
AB - Let [x] denote the integer part of x ∈ R, and let ∥x∥ denote the distance from x to the nearest integer. In this paper we prove that, whenever α is irrational number and β is any real number, then for any fixed \frac{47}{48}<γ <1, there exist infinitely many prime numbers p satisfying the inequality ∥αp^3 + β∥
ER -