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The distribution of rational points on hypersurfaces defined over a finite field

Published online by Cambridge University Press:  26 February 2010

R. A. Smith
R. A. Smith
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada.
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Extract

Let p be an odd prime and denote by [p] the field of p elements. Let C = C(n, p) be the set of points x = (x1 …, xn) of Zn (n ≥ 1) satisfying

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970 , pp. 328 - 332
Copyright
Copyright © University College London 1970

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References

1.Bombieri, E., “On exponential sums in finite fields”, Amer. J. Math., 88 (1966), 71–105.CrossRefGoogle Scholar
2.Bombieri, E., and Davenport, H., “On two problems of Mordell”, Amer. J. Math., 88 (1966), 61–70.CrossRefGoogle Scholar
3.Chalk, J. H. H., “The number of solutions of congruences in incomplete residue systems”, Canadian J. Math., 15 (1963), 291–296.CrossRefGoogle Scholar
4.Chalk, J. H. H., and Smith, R. A., “On Bombieri's estimates for exponential sums”, Acta Arith. (to appear).Google Scholar
5.Chalk, J. H. H., and Smith, R. A., and Williams, K. S., “The distribution of solutions of congruences”, Mathematika, 12 (1965), 176–192.CrossRefGoogle Scholar
6.Chalk, J. H. H., and Smith, R. A., and Williams, K. S., “The distribution of solutions of congruences, corrigendum and addendum”, Mathematika, 16 (1969), 98–100.CrossRefGoogle Scholar
7.Lang, S. and Weil, A., “Number of points on varieties in finite fields”, Amer. J. Math., 76 (1954), 819–827.CrossRefGoogle Scholar
8.Mordell, L. J., “On the number of solutions in incomplete residue sets of quadratic congruences”, Arch, der Math., 8 (1957), 153–157.CrossRefGoogle Scholar
9.Vinogradov, I. M., Elements of number theory (Dover, 1954).Google Scholar
10.Weil, A., Foundations of algebraic geometry, A.M.S. Coll. Publ., 29 (1946).Google Scholar