On some equations over finite fields

Ioulia Baoulina[1]

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

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 45-50
  • ISSN: 1246-7405

Abstract

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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 .

How to cite

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Baoulina, Ioulia. "On some equations over finite fields." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 45-50. <http://eudml.org/doc/249448>.

@article{Baoulina2005,
abstract = {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 $q$.},
affiliation = {The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India},
author = {Baoulina, Ioulia},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {finite field; Markoff-Hurwitz equation; Gauss sum},
language = {eng},
number = {1},
pages = {45-50},
publisher = {Université Bordeaux 1},
title = {On some equations over finite fields},
url = {http://eudml.org/doc/249448},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Baoulina, Ioulia
TI - On some equations over finite fields
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 45
EP - 50
AB - 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 $q$.
LA - eng
KW - finite field; Markoff-Hurwitz equation; Gauss sum
UR - http://eudml.org/doc/249448
ER -

References

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  1. I. Baoulina, On the Problem of Explicit Evaluation of the Number of Solutions of the Equation a 1 x 1 2 + ⋯ + a n x n 2 = b x 1 ⋯ 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. Zbl1086.11021MR1925639
  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. Zbl0906.11001MR1625181
  4. L. Carlitz, Certain special equations in a finite field. Monatsh. Math. 58 (1954), 5–12. Zbl0055.26803MR61121

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