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Session S26 - Finite fields and applications

Friday, July 16, 14:00 ~ 14:20 UTC-3

On diagonal equations over finite fields via walks in NEPS of graphs

Denis Videla

Universidad Nacional de Córdoba, Argentina - denisv458@gmail.com

We obtain an explicit combinatorial formula for the number of solutions $(x_1,\ldots,x_r)\in \mathbb{F}_{p^{ab}}$ to the diagonal equation $x_{1}^k+\cdots+x_{r}^k=\alpha$ over the finite field $\mathbb{F}_{p^{ab}}$ , with $k=\frac{p^{ab}-1}{b(p^a-1)}$ and $b>1$ by using the number of $r$ -walks in NEPS of complete graphs. This talk is based on a recent accepted article.

\textsc{Denis E.\@ Videla}. \textit{On diagonal equations over finite fields via walks in NEPS of graphs}. Finite Fields Appl. (2021), accepted, https://arxiv.org/abs/1907.03145

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