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

Note on the Kloosterman sum


Author: Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 30 (1971), 61-62
MSC: Primary 10.41
MathSciNet review: 0285501
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Abstract: The Kloosterman sum

$\displaystyle \sum\limits_{x = 0;(x,p) = 1}^{{p^\alpha } - 1} {\exp (2\pi in(x + \bar x)/{p^\alpha }),} $

where p is an odd prime, $ \alpha \geqq 2$ and $ (n,p) = 1$, is evaluated in a very short direct way.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0285501-3
PII: S 0002-9939(1971)0285501-3
Article copyright: © Copyright 1971 American Mathematical Society