Exponential sums on reduced residue systems. (English) Zbl 0944.11025

Loh, W. K. A.

Can. Math. Bull. 41, No. 2, 187-195 (1998).

Author’s abstract: ”The aim of this article is to obtain an upper bound for the exponential sum \(\sum e(f(x)/q)\), where the summation runs from \(x=1\) to \(x=q\) with \((x,q)=1\) and \(e(\alpha)\) denotes \(\exp(2 \pi i \alpha)\). We shall show that the upper bound depends only on the values of \(q\) and \(s\), where \(s\) is the number of terms in the polynomial \(f(x)\).” The proof makes use of some ideas developed by J. H. Loxton and R. C. Vaughan [Can. J. Math. 28, 440-454 (1985; Zbl 0575.10033)].

Reviewer: J.Hinz (Marburg)

MSC:

11L07

Estimates on exponential sums

Keywords:

upper bound; exponential sum

Citations:

Zbl 0575.10033