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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

High order moments of character sums


Authors: Todd Cochrane and Zhiyong Zheng
Journal: Proc. Amer. Math. Soc. 126 (1998), 951-956
MSC (1991): Primary 11L40, 11D79
MathSciNet review: 1473660
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish the upper bound

\begin{equation*}\frac{1}{p-1} \sum _{\chi \ne \chi _{o}}\big | \sum _{x=a+1}^{a+B} \chi (x) \big |^{2k} \ll _{\epsilon ,k} p^{k-1 +\epsilon } + B^{k} p^{\epsilon }, \end{equation*}

with $p$ a prime and $k$ any positive integer, the sum being over all nonprincipal multiplicative characters $\pmod p$.


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Additional Information

Todd Cochrane
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: cochrane@math.ksu.edu

Zhiyong Zheng
Affiliation: Department of Mathematics, Zhongshan University, Guangzhou 510275, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04625-5
PII: S 0002-9939(98)04625-5
Keywords: Character sums, congruences
Received by editor(s): February 25, 1996
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1998 American Mathematical Society