COUNTING POINTS ON DWORK HYPERSURFACES AND -ADIC HYPERGEOMETRIC FUNCTIONS

DOI10.1017/S0004972715001847zbMATH Open1418.11102arXiv1511.09192OpenAlexW3102388266MaRDI QIDQ2986532

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Publication date: 16 May 2017

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Abstract: We express the number of points on the Dwork hypersurface ${\displaystyle }$X_{lambda}^d: x_1^d+x_2^d+cdots +x_d^d=dlambda x_1x_2cdots x_d${\displaystyle }$ over a finite field of order $qotequiv1pmodd$ in terms of McCarthy's $p$-adic hypergeometric function for any odd prime $d$.

Full work available at URL: https://arxiv.org/abs/1511.09192

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