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Matematicheskie Zametki, 2010, Volume 88, Issue 4, Pages 620–624
DOI: https://doi.org/10.4213/mzm8851 (Mi mzm8851) 		 
This article is cited in 8 scientific papers (total in 8 papers)

A Supercongruence Motivated by the Legendre Family of Elliptic Curves

Heng Huat Chana, Ling Longb, W. Zudilinc

a National University of Singapore
b Iowa State University, USA
c University of Newcastle, Australia
Full-text PDF (397 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm8851
Abstract: A new supercongruence associated with a Gaussian hypergeometric series, as well as one of Mortenson's supercongruences, are established with new congruence relations and the Legendre transforms of certain sequences.
Keywords: elliptic curve, ramified double cover, finite field, Hasse invariant, supercongruence, Legendre transform.
Received: 24.01.2010
English version:
Mathematical Notes, 2010, Volume 88, Issue 4, Pages 599–602
DOI: https://doi.org/10.1134/S0001434610090324
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
Citation: Heng Huat Chan, Ling Long, W. Zudilin, “A Supercongruence Motivated by the Legendre Family of Elliptic Curves”, Mat. Zametki, 88:4 (2010), 620–624; Math. Notes, 88:4 (2010), 599–602
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm8851
  • https://doi.org/10.4213/mzm8851
  • https://www.mathnet.ru/eng/mzm/v88/i4/p620
    • This publication is cited in the following 8 articles:
    1. Michael Allen, “On some hypergeometric supercongruence conjectures of Long”, Ramanujan J, 61:3 (2023), 957  crossref
    2. Long L., Tu F.-T., Yui N., Zudilin W., “Supercongruences For Rigid Hypergeometric Calabi-Yau Threefolds”, Adv. Math., 393 (2021), 108058  crossref  mathscinet  isi
    3. Guo V.J.W., “Factors of Some Truncated Basic Hypergeometric Series”, J. Math. Anal. Appl., 476:2 (2019), 851–859  crossref  mathscinet  zmath  isi  scopus
    4. Liu J.-C., “Congruences For Truncated Hypergeometric Series F-2(1)”, Bull. Aust. Math. Soc., 96:1 (2017), 14–23  crossref  mathscinet  zmath  isi  scopus
    5. Kibelbek J., Long L., Moss K., Sheller B., Yuan H., “Supercongruences and complex multiplication”, J. Number Theory, 164 (2016), 166–178  crossref  mathscinet  zmath  isi  scopus
    6. Deines A., Fuselier J.G., Long L., Swisher H., Tu F.-T., “Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions”, Directions in Number Theory, Association For Women in Mathematics Series, 3, eds. Eischen E., Long L., Pries R., Stange K., Springer International Publishing Ag, 2016, 125–159  crossref  mathscinet  zmath  isi  scopus
    7. Guo V.J.W., Zeng J., “Some Q-Analogues of Supercongruences of Rodriguez-Villegas”, J. Number Theory, 145 (2014), 301–316  crossref  mathscinet  zmath  isi  scopus
    8. Long L., “Hypergeometric evaluation identities and supercongruences”, Pacific J. Math., 249:2 (2011), 405–418  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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