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Counting Points on Dwork Hypersurfaces and $p$-adic Gamma Function (1511.09192v1)
Published 30 Nov 2015 in math.NT
Abstract: We express the number of points on the Dwork hypersurface $$X_{\lambda}d: x_1d+x_2d+\cdots +x_dd=d\lambda x_1x_2\cdots x_d$$ 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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