Note on the Kloosterman Sum

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Sep 1971Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 30, page 61 (issn: 0002-9939,

Copyright policy )

Authors: Williams, K. S.;

doi: 10.2307/2038221 , 10.1090/s0002-9939-1971-0285501-3

Note on the Kloosterman Sum

- Summary
- Subjects
- Metrics

Abstract

The Kloosterman sum \[ ∑ x = 0 ; ( x , p ) = 1 p α − 1 exp ⁡ ( 2 π i n ( x + x ¯ ) / p α ) , \sum \limits _{x = 0;(x,p) = 1}^{{p^\alpha } - 1} {\exp (2\pi in(x + \bar x)/{p^\alpha }),} \] where p is an odd prime, α ≧ 2 \alpha \geqq 2 and ( n , p ) = 1 (n,p) = 1 , is evaluated in a very short direct way.

Keywords

Gauss and Kloosterman sums; generalizations

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	6
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average