English

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.

Keywords

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