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

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

Zbl 0575.10033
Full Text: