Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2010; 47(5): 947-965

Printed September 1, 2010

https://doi.org/10.4134/JKMS.2010.47.5.947

Copyright © The Korean Mathematical Society.

Inversion of $L$-functions, general Kloosterman sums weighted by incomplete character sums

Xiaobeng Zhang and Huaning Liu

Northwest University

Abstract

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, $2$-th power mean of the inversion of Dirichlet $L$-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

Keywords: character sum, $L$-function, general Kloosterman sum, asymptotic formula

MSC numbers: 11L05