Counting Points on Dwork Hypersurfaces and $p$-adic Gamma Function

Rupam Barman; Hasanur Rahman; Neelam Saikia

doi:10.1017/s0004972715001847

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arXiv · 1511.09192

Counting Points on Dwork Hypersurfaces and $p$-adic Gamma Function

Rupam Barman·Hasanur Rahman·Neelam Saikia

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Abstract

We express the number of points on the Dwork hypersurface $$X_λ^d: x_1^d+x_2^d+\cdots +x_d^d=dλx_1x_2\cdots x_d$$ over a finite field of order $q \not \equiv 1 \pmod{d}$ in terms of McCarthy's $p$-adic hypergeometric function for any odd prime $d$.

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Rupam Barman, Hasanur Rahman, Neelam Saikia. 2015-11-30. Counting Points on Dwork Hypersurfaces and $p$-adic Gamma Function. https://doi.org/10.1017/s0004972715001847

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