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Bulletin of the London Mathematical Society 2001 33(1):16-24; doi:10.1112/blms/33.1.16
© 2001 by London Mathematical Society
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© London Mathematical Society

On the Number of Solutions of an Equation Over a Finite Field

J. W. P. Hirschfeld and G. Korchmáros

School of Mathematical Sciences, University of Sussex Brighton BN1 9QH; e-mail: jwph{at}sussex.ac.uk
Dipartimento di Matematica, Università della Basilicata 85100 Potenza, Italy; e-mail: korchmaros{at}unibas.it

Received 14 December 1998. Revision received 4 October 1999. Revision received 2 February 2000.

The Stöhr–Voloch approach is used to obtain a new bound for the number of solutions in (Fq)2 of an equation f(X, Y) = 0, where f(X, Y) is an absolutely irreducible polynomial with coefficients in a finite field Fq.


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