ON THE NUMBER OF SOLUTIONS TO CERTAIN DIAGONAL EQUATIONS OVER FINITE FIELDS-Reference-Cited by-同舟云学术

ON THE NUMBER OF SOLUTIONS TO CERTAIN DIAGONAL EQUATIONS OVER FINITE FIELDS

Published:2010-02 Issue:01 Volume:06 Page:1-14
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BAOULINA IOULIA¹

Affiliation:

1. Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India

Abstract

We consider a diagonal equation, which can be reduced to the form [Formula: see text] over a finite field of characteristic p > 2. In 1997, Sun obtained the explicit formula for the number of solutions to an equation of this type when n is even. In this paper, we find explicit formulas for the number of solutions when n is odd, k = 2rh, and there exists a positive integer ℓ such that pℓ ≡ 2m-1h + 1 ( mod 2mh), m = 3 or 4, r ≥ m, h = 1 or 3.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042110002776

Reference14 articles.

1. On the pure Jacobi sums

2. Generalizations of the Markoff–Hurwitz equations over finite fields

3. ON THE EQUATION $(x_1^{m_1}+\cdots+x_n^{m_n})^k=ax_1\cdots x_n$ OVER A FINITE FIELD

4. Sums of Gauss, Eisenstein, Jacobi, Jacobsthal, and Brewer

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