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arXiv · 1608.05697

The number of $\mathbb{F}_p$-points on Dwork hypersurfaces and hypergeometric functions

Dermot McCarthy
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Abstract

We provide a formula for the number of $\mathbb{F}_{p}$-points on the Dwork hypersurface $$x_1^n + x_2^n \dots + x_n^n - n \lambda \, x_1 x_2 \dots x_n=0$$ in terms of a $p$-adic hypergeometric function previously defined by the author. This formula holds in the general case, i.e for any $n, \lambda \in \mathbb{F}_p^{*}$ and for all odd primes $p$, thus extending results of Goodson and Barman et al which hold in certain special cases.

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Dermot McCarthy. 2016-08-19. The number of $\mathbb{F}_p$-points on Dwork hypersurfaces and hypergeometric functions. https://arxiv.org/abs/1608.05697

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