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arXiv · 1602.01807

On a class of diagonal equations over finite fields

Ioulia N. Baoulina
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Abstract

Using properties of Gauss and Jacobi sums, we derive explicit formulas for the number of solutions to a diagonal equation of the form $x_1^{2^m}+\dots+x_n^{2^m}=0$ over a finite field of characteristic $p\equiv\pm 3\pmod{8}$. All of the evaluations are effected in terms of parameters occurring in quadratic partitions of some powers of $p$.

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Ioulia N. Baoulina. 2016-02-04. On a class of diagonal equations over finite fields. https://doi.org/10.1016/j.ffa.2016.04.005

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