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On the Number of Zeros Over a Finite Field of Certain Symmetric Polynomials

Published online by Cambridge University Press:  20 November 2018

P. V. Ceccherini  and
J. W. P. Hirschfeld
P. V. Ceccherini
Affiliation:
Università Di Roma, 00100 Roma, Italy
J. W. P. Hirschfeld
Affiliation:
University Of Sussex, Brighton, U.K. BN1 9QH
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A variety of applications depend on the number of solutions of polynomial equations over finite fields. Here the usual situation is reversed and we show how to use geometrical methods to estimate the number of solutions of a non-homogeneous symmetric equation in three variables.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 327 - 332
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Barlotti, A., Un estensione del teorema di Segre-Kustaanheimo, Boll. Un. Mat. Ital. 10 (1955), 96-98.Google Scholar
2. Hirschfeld, J. W. P., Ovals in Desarguesian planes of even order, Ann. Mat Pura. Appl. 102 (1975), 79-89.Google Scholar
3. Hirschfeld, J. W. P., Projective geometries over finite fields, Oxford Univ. Press, 1979.Google Scholar
4. Segre, B., Lectures on modem geometry, Cremonese, Rome, 1961.Google Scholar
5. Segre, B., Introduction to Galois geometries, Atti Accad. Naz. Lincei Mem. 8 (1967), 133-236.Google Scholar
6. Tits, J., Ovoides et groupes de Suzuki, Arch. Math. 13 (1962), 187-198.Google Scholar