High order moments of character sums
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- by Todd Cochrane and Zhiyong Zheng PDF
- Proc. Amer. Math. Soc. 126 (1998), 951-956 Request permission
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 $\pmod p$.References
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Additional Information
- Todd Cochrane
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- MR Author ID: 227122
- Email: cochrane@math.ksu.edu
- Zhiyong Zheng
- Affiliation: Department of Mathematics, Zhongshan University, Guangzhou 510275, Peopleβs Republic of China
- Received by editor(s): February 25, 1996
- Communicated by: Dennis A. Hejhal
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 951-956
- MSC (1991): Primary 11L40, 11D79
- DOI: https://doi.org/10.1090/S0002-9939-98-04625-5
- MathSciNet review: 1473660