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On Salié's sum

Published online by Cambridge University Press:  18 May 2009

L. J. Mordell
L. J. Mordell
Affiliation:
St. John's College, Cambridge
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Let p be an odd prime and let f(x) be a complex-valued function such that f(x+p) = f(x) for all integers x. Write e(x) = exp(2πix/p), and define l/x by , where We consider the sum

where is the Legendre symbol. The sum is zero if as is clear on replacing x by bjax. Salié has found a result which can be written in the form

when h2 ≡ 4ab(modp).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 1 , February 1973 , pp. 25 - 26
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Mordell, L. J., On some exponential sums related to Kloosterman sums, Ada Arithmetical to appear.Google Scholar
2.Williams, K. S., On Salié's sum, J. Number Theory 3 (1971), 316–317.CrossRefGoogle Scholar