Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1971-0285501-3
MathSciNet review: 0285501
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] L. Carlitz, A note on multiple Kloosterman sums, J. Indian Math. Soc. 29 (1965), 197-200. MR 34 #2532. MR 0202672 (34:2532)
  • [2] T. Estermann, On Kloosterman's sum, Mathematika 8 (1961), 83-86. MR 23 #A3716. MR 0126420 (23:A3716)
  • [3] H. Salié, Über die Kloostermanschen Summen $ S(u,v;q)$, Math. Z. 34 (1931), 91-109.
  • [4] A. L. Whiteman, A note on Kloosterman sums, Bull. Amer. Math. Soc. 51 (1945), 373-377. MR 6, 259. MR 0012105 (6:259f)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10.41

Retrieve articles in all journals with MSC: 10.41


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0285501-3
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society