This article is cited in 8 papers

A Supercongruence Motivated by the Legendre Family of Elliptic Curves

Heng Huat Chan^a, Ling Long^b, W. Zudilin<sup>c

a</sup> National University of Singapore
^b Iowa State University, USA
^c University of Newcastle, Australia

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.

UDC: 511

Received: 24.01.2010

DOI: 10.4213/mzm8851

 English version: Mathematical Notes, 2010, 88:4, 599–602

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