Glasnik Matematicki, Vol. 44, No.2 (2009), 333-342.

ON CERTAIN CHARACTER SUMS OVER SMOOTH NUMBERS

Ke Gong

Department of Mathematics, Tongji University, Shanghai 200092, P. R. China
e-mail: kogong@gmail.com

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

∑n in 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.

2000 Mathematics Subject Classification.   11L40, 11L20, 11N25.

Key words and phrases.   Character sums, rational functions, smooth numbers.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.2.06

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