A remark on the distribution of $\sqrt{p}$ modulo one involving primes of special type
Abstract
Let $P_r$ denote an integer with at most $r$ prime factors counted with multiplicity. In this paper we prove that for any $0 \lt \lambda \lt \frac{1}{4}$, the inequality $\{\sqrt{p}\}\lt p ^{-\lambda}$ has infinitely many solutions in primes $p$ such that $p + 2 = P_r$, where $r = \lfloor \frac{8}{1-4\lambda} \rfloor$. This generalizes the previous result of Cai.
Fields of Study & Subjects
Analytic Number Theory Research
Publication details
- Journal / source
- Hiroshima Mathematical Journal
- Publisher
- Hiroshima University - Department of Mathematics
- Volume
- 56
- Issue
- 1
- Pages
- 57-60
- Publication date
- 1 March 2026
- Language
- EN