FRACTIONAL PARTS OF POLYNOMIALS OVER THE PRIMES. Issue 3 (29th November 2017) - Baker, Roger
Abstract : Let f be a polynomial of degree k > 1 with irrational leading coefficient. We obtain results of the form ∥ f ( p ) ∥ < p − σ for infinitely many primes p that supersede those of Harman [Trigonometric sums over primes I. Mathematika 28 (1981), 249–254; Trigonometric sums over primes II. Glasg. Math. J. 24 (1983), 23–37] and Wong [On the distribution of α p k modulo 1. Glasg. Math. J. 39 (1997), 121–130].