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.

**[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*, 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****[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

Keywords:
Exponential sum,
Legendre symbol,
Salié's sum,
Gauss sum

Article copyright:
© Copyright 1971
American Mathematical Society