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A finite evaluation of a special exponential sum

Published online by Cambridge University Press:  24 October 2008

L. J. Mordell
L. J. Mordell
Affiliation:
St John's College, Cambridge
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Extract

Let f(x) and g(x) be rational functions of x with integer coefficients, p an odd prime, e(x) = e(2πix/p), e(u/v) = e(w), where u = vw (mod p)† and χ(x) is a character mod p. It is well known that very abstruse methods are required to find an estimate for sums such as

where in the summation, ‡ the values of x are omitted for which eitherf(x) or g(x) is not defined.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 1 , January 1972 , pp. 75 - 78
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Salié, H.Über die Kloostermanschen Summen S(u, v, q). Math. Z. 34 (1931), 91.CrossRefGoogle Scholar