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COUNTING POINTS ON DWORK HYPERSURFACES AND
$p$-ADIC HYPERGEOMETRIC FUNCTIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 94 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 17 February 2016, pp. 208-216
- Print publication:
- October 2016
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- Article
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- You have access
- Export citation
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We express the number of points on the Dwork hypersurface
$X_{\unicode[STIX]{x1D706}}^{d}:x_{1}^{d}+x_{2}^{d}+\cdots +x_{d}^{d}=d\unicode[STIX]{x1D706}x_{1}x_{2}\cdots x_{d}$ over a finite field of order 
$q\not \equiv 1\,(\text{mod}\,d)$ in terms of McCarthy’s 
$p$-adic hypergeometric function for any odd prime 
$d$.
