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On Kloosterman Sums with Oscillating Coefficients

Published online by Cambridge University Press:  20 November 2018

Peiming Deng
Peiming Deng*
Affiliation:
Department of Mathematics The Normal University of Guangxi Guilin, Guangxi 541004 P.R. China
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Abstract

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In this paper we prove: for any positive integers $a$ and $q$ with $\left( a,\,q \right)\,=\,1$, we have uniformly

$$\sum\limits_{\begin{matrix} n\le N \\ (n,q)=1,n\bar{n}\equiv 1(\,\bmod \,q) \\ \end{matrix}}{\mu (n)e(\frac{a\bar{n}}{q})\ll Nd(q)\left\{ \frac{{{\log }^{\frac{5}{2}}}N}{{{q}^{\frac{1}{2}}}}+\frac{{{q}^{\frac{1}{5}}}{{\log }^{\frac{13}{5}}}N}{{{N}^{\frac{1}{5}}}} \right\}.}$$

This improves the previous bound obtained by D. Hajela, A. Pollington and B. Smith [5].

Keywords

10G10Kloosterman sumsoscillating coefficientsestimate
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 285 - 290
Copyright
Copyright © Canadian Mathematical Society 1999

References

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