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Weighted Quadratic PartitionsOver a Finite Field

Published online by Cambridge University Press:  20 November 2018

Leonard Carlitz
Leonard Carlitz*
Affiliation:
Duke University
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Using some known results on Gauss sums in a finite field, it is shown that the sum (1.3) defined below can either be evaluated explicitly or expressed in terms of a Kloosterman sum. The same result applies to the more general sum S(α, λ, Q) defined in (5.1). The latter sum also satisfies the reciprocity formula (5.5). Some related sums are discussed in §§6, 7.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 317 - 323
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Bôcher, M., Higher algebra (New York, 1924).Google Scholar
2. Carlitz, L., The singular series for sums of squares of polynomials, Duke Math. J., 14 (1947), 1105–1120.Google Scholar
3. Dickson, L. E., Linear groups (Leipzig, 1901).Google Scholar
4. Salie, H., Über die Kloostermanschen Summen S(u, v; q), Math. Z., 34 (1932), 91–109.Google Scholar
5. Weil, André, On some exponential sums, Proc. Nat. Acad. Sci., 34 (1948), 204–207.Google Scholar