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The Kloosterman Sum Revisited

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Carleton University, Ottawa, Canada
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Let p be an odd prime, n an integer not divisible by p and α a positive integer. For any integer h with (h,pα)=l, is defined as any solution of the congruence (mod,pα). The Kloosterman sum Ap α(n) (see for example [4]) is defined by

(1.1)

where the dash (') indicates that the letter of summation runs only through a reduced residue system with respect to the modulus.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 363 - 365
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers, Oxford Univ. Press, London, (1962), p. 237.Google Scholar
2. Salie, H., Uber die Kloostermanschen Summen S(u, v; q), Math. Z. 34 (1931), 91–109.Google Scholar
3. Weil, A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204–207.Google Scholar
4. Whiteman, A. L., A note on Kloosterman sums, Bull. Amer. Math. Soc, 51 (1945), 373–377.Google Scholar
5. Williams, K. S., Note on the Kloosterman sum, Proc. Amer. Math. Soc. 30 (1971), 61–62.Google Scholar