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

Published online by Cambridge University Press:  17 February 2016

RUPAM BARMAN*
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India email rupam@maths.iitd.ac.in
HASANUR RAHMAN
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India email hasrah93@gmail.com
NEELAM SAIKIA
Affiliation:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India email nlmsaikia1@gmail.com
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Abstract

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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 $d$.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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