Mots-clés : Hasse invariant, Legendre transform.
@article{MZM_2010_88_4_a12,
author = {Heng Huat Chan and Ling Long and W. Zudilin},
title = {A {Supercongruence} {Motivated} by the {Legendre} {Family} of {Elliptic} {Curves}},
journal = {Matemati\v{c}eskie zametki},
pages = {620--624},
year = {2010},
volume = {88},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a12/}
}
Heng Huat Chan; Ling Long; W. Zudilin. A Supercongruence Motivated by the Legendre Family of Elliptic Curves. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 620-624. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a12/
[1] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math., 106, Springer-Verlag, New York, 1986 | MR | Zbl
[2] C. H. Clemens, A Scrapbook of Complex Curve Theory, Univ. Ser. Math., Plenum Press, New York, 1980 | MR | Zbl
[3] R. Osburn, C. Schneider, “Gaussian hypergeometric series and supercongruences”, Math. Comp., 78:265 (2009), 275–292 | MR
[4] W. Zudilin, “Ramanujan-type supercongruences”, J. Number Theory, 129:8 (2009), 1848–1857 | DOI | MR | Zbl
[5] S. Ahlgren, K. Ono, “A Gaussian hypergeometric series evaluation and Apéry number congruences”, J. Reine Angew. Math., 518 (2000), 187–212 | MR | Zbl
[6] D. McCarthy, R. Osburn, “A $p$-adic analogue of a formula of Ramanujan”, Arch. Math. (Basel), 91:6 (2008), 492–504 | MR | Zbl
[7] E. Mortenson, “A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function”, J. Number Theory, 99:1 (2003), 139–147 | DOI | MR | Zbl
[8] E. Mortenson, “Supercongruences between truncated ${}_2F_1$ hypergeometric functions and their Gaussian analogs”, Trans. Amer. Math. Soc., 355:3 (2003), 987–1007 | DOI | MR | Zbl