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Estimates for multiple exponential sums

Published online by Cambridge University Press:  09 April 2009

John H. Loxton  and
Robert A. Smith
John H. Loxton
Affiliation:
Department of Mathematics University of New South WalesKensington, N.S.W. 2033, Australia
Robert A. Smith
Affiliation:
Department of Mathematics University of TorontoToronto, Ontario M5S 1A1, Canada
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Abstract

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We give estimates for exponential sums of the shape , where F is a polynomial with interger coefficient and each component of (x1,…, xn) in the sum runs through a complete set of residues modulo q.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 125 - 134
Copyright
Copyright © Australian Mathematical Society 1982

References

1.Davenport, H., ‘Cubic forms in 32 variables,’ Philos. Trans. Roy. Soc. London Ser. A, 251 (1959), 193–232.Google Scholar
2.Deligne, P., ‘La conjecture de Weil, I,’ Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307.CrossRefGoogle Scholar
3.Igusa, J.-I., Lectures on forms of higher degree (Tata Institute of Fundamental Research, Bombay, 1978).Google Scholar
4.Loxton, J. H. and Smith, R. A., ‘On Hua's estimate for exponential sums,’ to appear.Google Scholar
5.Nagell, T., Introduction to number theory (Wiley, New York, 1951).Google Scholar
6.Sándor, G., ‘Über die Anzahl der Lösungen einer Kongruenz,’ Acta Math. 87 (1952), 13–17.CrossRefGoogle Scholar
7.Shafarevich, I. R., Basic algebraic geometry (Springer-Verlag, Berlin/New York, 1977).Google Scholar
8.Smith, R. A., ‘Estimates for exponential sums,’ Proc. Amer. Math. Soc. 79 (1980), 365–368.CrossRefGoogle Scholar
9.van der Waerden, B. L., Modern Algebra, vol. II, (Ungar, New York, 1950).Google Scholar