Abstract view
|
On Kloosterman Sums with Oscillating Coefficients
|
|
Published:1999-09-01
Printed: Sep 1999
Abstract
In this paper we prove: for any positive integers $a$ and $q$ with
$(a,q) =1$, we have uniformly
$$
\sum_{\substack{n \leq N \\ (n,q) = 1, \,n\on \equiv 1 (\mod q)}}
\mu (n) e \left( \frac{a\on}{q} \right) \ll Nd (q) \left\{
\frac{\log^{\frac52} N}{q^{\frac12}} + \frac{q^{\frac15}
\log^{\frac{13}5} N}{N^{\frac15}} \right\}.
$$
This improves the previous bound obtained by D.~Hajela,
A.~Pollington and B.~Smith~\cite{5}.
