COUNTING POINTS ON DWORK HYPERSURFACES AND $p$ -ADIC HYPERGEOMETRIC FUNCTIONS

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 a...

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Bibliographic Details
Published inBulletin of the Australian Mathematical Society Vol. 94; no. 2; pp. 208 - 216
Main Authors BARMAN, RUPAM, RAHMAN, HASANUR, SAIKIA, NEELAM
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.10.2016
Subjects
hypergeometric series
Teichmüller character
Dwork hypersurfaces
33E50
characters of finite fields
p-adic gamma function
primary 11G25
33C20
secondary 11S80
11T24
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Summary: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 $d$ .
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972715001847