$p$-Adic hypergeometric functions and the trace of Frobenius of elliptic curves Article Swipe
Sulakashna
,
Rupam Barman
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2311.03259
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2311.03259
Let $p$ be an odd prime and $q=p^r$, $r\geq 1$. For positive integers $n$, let ${_n}G_n[\cdots]_q$ denote McCarthy's $p$-adic hypergeometric functions. In this article, we prove an identity expressing a ${_4}G_4[\cdots]_q$ hypergeometric function as a sum of two ${_2}G_2[\cdots]_q$ hypergeometric functions. This identity generalizes some known identities satisfied by the finite field hypergeometric functions. We also prove a transfomation that relates ${_{n+2}}G_{n+2}[\cdots]_q$ and ${_n}G_n[\cdots]_q$ hypergeometric functions. Next, we express the trace of Frobenius of elliptic curves in terms of special values of ${_4}G_4[\cdots]_q$ and ${_6}G_6[\cdots]_q$ hypergeometric functions. Our results extend the recent works of Tripathi and Meher on the finite field hypergeometric functions to wider classes of primes.
Related Topics
Concepts
Hypergeometric function
Basic hypergeometric series
Mathematics
Generalized hypergeometric function
TRACE (psycholinguistics)
Hypergeometric identity
Hypergeometric distribution
Identity (music)
Confluent hypergeometric function
Pure mathematics
Field (mathematics)
Elliptic curve
Hypergeometric function of a matrix argument
Physics
Linguistics
Philosophy
Acoustics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2311.03259
- https://arxiv.org/pdf/2311.03259
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4388482141
All OpenAlex metadata
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https://openalex.org/W4388482141Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2311.03259Digital Object Identifier
- Title
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$p$-Adic hypergeometric functions and the trace of Frobenius of elliptic curvesWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-11-06Full publication date if available
- Authors
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Sulakashna, Rupam BarmanList of authors in order
- Landing page
-
https://arxiv.org/abs/2311.03259Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2311.03259Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2311.03259Direct OA link when available
- Concepts
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Hypergeometric function, Basic hypergeometric series, Mathematics, Generalized hypergeometric function, TRACE (psycholinguistics), Hypergeometric identity, Hypergeometric distribution, Identity (music), Confluent hypergeometric function, Pure mathematics, Field (mathematics), Elliptic curve, Hypergeometric function of a matrix argument, Physics, Linguistics, Philosophy, AcousticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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