Fractional parts of polynomials over the primes
Number Theory
2017-12-21 v2
Abstract
Let f be a polynomial with irrational leading coefficient. We obtain inequalities for the distance from the nearest integer of f(p) that hold for infinitely many primes p. These results improve work of Harman in 1981 and 1983 and Wong in 1997.
Cite
@article{arxiv.1606.05779,
title = {Fractional parts of polynomials over the primes},
author = {Roger Baker},
journal= {arXiv preprint arXiv:1606.05779},
year = {2017}
}
Comments
Some corrections; this version to appear in Mathematika memorial issue for Klaus Roth