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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on Salié's sum


Author: Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 30 (1971), 393-394
MSC: Primary 10.41
MathSciNet review: 0284408
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Abstract: It is shown in a very simple way that an exponential sum (involving the Legendre symbol) considered by Salié is the sum of two Gauss sums.


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

  • [1] L. J. Mordell, On some exponential sums related to Kloosterman sums (submitted for publication).
  • [2] -, On Salié's sum (submitted for publication).
  • [3] H. Salié, Über die Kloostermanschen Summen $ S(u,v;q)$, Math. Z. 34 (1931), 91-109.
  • [4] Kenneth S. Williams, Finite transformation formulae involving the Legendre symbol, Pacific J. Math. 34 (1970), 559–568. MR 0269618 (42 #4513)
  • [5] -, On Salié's sum, J. Number Theory 3 (1971).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0284408-5
PII: S 0002-9939(1971)0284408-5
Keywords: Exponential sum, Legendre symbol, Salié's sum, Gauss sum
Article copyright: © Copyright 1971 American Mathematical Society