Note on the Kloosterman sum
HTML articles powered by AMS MathViewer
- by Kenneth S. Williams PDF
- Proc. Amer. Math. Soc. 30 (1971), 61-62 Request permission
Abstract:
The Kloosterman sum \[ \sum \limits _{x = 0;(x,p) = 1}^{{p^\alpha } - 1} {\exp (2\pi in(x + \bar x)/{p^\alpha }),} \] where p is an odd prime, $\alpha \geqq 2$ and $(n,p) = 1$, is evaluated in a very short direct way.References
- L. Carlitz, A note on multiple Kloosterman sums, J. Indian Math. Soc. (N.S.) 29 (1965), 197–200. MR 202672
- T. Estermann, On Kloosterman’s sum, Mathematika 8 (1961), 83–86. MR 126420, DOI 10.1112/S0025579300002187 H. Salié, Über die Kloostermanschen Summen $S(u,v;q)$, Math. Z. 34 (1931), 91-109.
- Albert Leon Whiteman, A note on Kloosterman sums, Bull. Amer. Math. Soc. 51 (1945), 373–377. MR 12105, DOI 10.1090/S0002-9904-1945-08356-6
Additional Information
- © Copyright 1971 American Mathematical Society
- 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