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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| Published in | Bulletin of the Australian Mathematical Society Vol. 94; no. 2; pp. 208 - 216 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.10.2016
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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
$d$
. |
|---|---|
| AbstractList | 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
$d$
. |
| Author | RAHMAN, HASANUR BARMAN, RUPAM SAIKIA, NEELAM |
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| Copyright | 2016 Australian Mathematical Publishing Association Inc. |
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| DOI | 10.1017/S0004972715001847 |
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| DocumentTitleAlternate | Counting points on Dwork hypersurfaces and $p$ -adic hypergeometric functions R. Barman, H. Rahman and N. Saikia |
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| Keywords | 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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$X_{\unicode[STIX]{x1D706}}^{d}:x_{1}^{d}+x_{2}^{d}+\cdots... |
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| Title | COUNTING POINTS ON DWORK HYPERSURFACES AND $p$ -ADIC HYPERGEOMETRIC FUNCTIONS |
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