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2012 Elliptic curves, eta-quotients and hypergeometric functions
David Pathakjee, Zef RosnBrick, Eugene Yoong
Involve 5(1): 1-8 (2012). DOI: 10.2140/involve.2012.5.1

Abstract

The well-known fact that all elliptic curves are modular, proven by Wiles, Taylor, Breuil, Conrad and Diamond, leaves open the question whether there exists a nice representation of the modular form associated to each elliptic curve. Here we provide explicit representations of the modular forms associated to certain Legendre form elliptic curves 2E1(λ) as linear combinations of quotients of Dedekind’s eta-function. We also give congruences for some of the modular forms’ coefficients in terms of Gaussian hypergeometric functions.

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David Pathakjee. Zef RosnBrick. Eugene Yoong. "Elliptic curves, eta-quotients and hypergeometric functions." Involve 5 (1) 1 - 8, 2012. https://doi.org/10.2140/involve.2012.5.1

Information

Received: 3 May 2010; Revised: 22 April 2011; Accepted: 14 September 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1284.11072
MathSciNet: MR2924308
Digital Object Identifier: 10.2140/involve.2012.5.1

Subjects:
Primary: 11F11, 11F20, 11G05
Secondary: 11T24, 33C99

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.5 • No. 1 • 2012
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