Original scientific paper

https://doi.org/10.3336/gm.44.2.06

On certain character sums over smooth numbers

Ke Gong ; Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

Abstract

We give nontrivial bounds in various ranges for character sums of the form

∑n S(x,y) χ(R1(n))eq(R2(n)),

where χ is a nonprincipal multiplicative character modulo a prime q, R1 and R2 are rational functions modulo q, and S(x,y) is the set of positive integers n ≤ x that are divisible only by primes p ≤ y. We also give sharper bounds in some special cases.

Keywords

Character sums; rational functions; smooth numbers

Hrčak ID:

44050

URI

https://hrcak.srce.hr/44050

Publication date:

9.12.2009.

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