On certain exponential sums over primes

Abstract

Let f (x) be a real valued polynomial in x of degree k ≥ 4 with leading coefficient α. In this paper, we prove a non-trivial upper bound for the quantity| under(∑, p ≤ N) (log p) e (f (p)) | whenever the leading coefficient α of f (x) is of type 1. © 2009 Elsevier Inc. All rights reserved.