On some equations over finite fields

Baoulina, Ioulia

doi:10.5802/jtnb.475

Baoulina, Ioulia ¹

¹ The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India

Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 45-50.

Résumé
Abstract

Dans ce papier, suivant L. Carlitz, nous considérons des équations particulières à $n$ variables sur le corps fini à $q$ éléments. Nous obtenons des formules explicites pour le nombre de solutions de ces équations, sous une certaine condition sur $n$ et $q$ .

In this paper, following L. Carlitz we consider some special equations of $n$ variables over the finite field of $q$ elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on $n$ and $q$ .

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/jtnb.475

Affiliations des auteurs :

Baoulina, Ioulia ¹

¹ The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India

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Baoulina, Ioulia. On some equations over finite fields. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 45-50. doi : 10.5802/jtnb.475. https://www.numdam.org/articles/10.5802/jtnb.475/

Bibliographie
Cité par

[1] I. Baoulina, On the Problem of Explicit Evaluation of the Number of Solutions of the Equation $a_{1}^{} x_{1}^{2} + \dots + a_{n}^{} x_{n}^{2} = b x_{1}^{} \dots x_{n}^{}$ in a Finite Field. In Current Trends in Number Theory, Edited by S. D. Adhikari, S. A. Katre and B. Ramakrishnan, Hindustan Book Agency, New Delhi, 2002, 27–37. | MR | Zbl

[2] A. Baragar, The Markoff Equation and Equations of Hurwitz. Ph. D. Thesis, Brown University, 1991.

[3] B. C. Berndt, R. J. Evans, K. S. Williams, Gauss and Jacobi Sums. Wiley-Interscience, New York, 1998. | MR | Zbl

[4] L. Carlitz, Certain special equations in a finite field. Monatsh. Math. 58 (1954), 5–12. | MR | Zbl

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