On Kloosterman Sums with Oscillating Coefficients

Canadian mathematical bulletin

关键词: Kloosterman sums;    oscillating coefficients;    estimate;   

DOI  :  10.4153/CMB-1999-034-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we prove: for any positive integers $a$ and $q$ with$(a,q) =1$, we have uniformly$$sum_{substack{n leq N \ (n,q) = 1, ,non equiv 1 (mod q)}}mu (n) e left( frac{aon}{q} ight) ll Nd (q) left{frac{log^{frac52} N}{q^{frac12}} + frac{q^{frac15}log^{frac{13}5} N}{N^{frac15}} ight}.$$This improves the previous bound obtained by D.~Hajela,A.~Pollington and B.~Smith~cite{5}.

【 授权许可】

Unknown