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The Ramanujan-Serre differential operators and certain elliptic curves


Authors: Masanobu Kaneko and Yuichi Sakai
Journal: Proc. Amer. Math. Soc. 141 (2013), 3421-3429
MSC (2010): Primary 11F11, 11F25; Secondary 11G05, 11F20
DOI: https://doi.org/10.1090/S0002-9939-2013-11917-9
Published electronically: June 26, 2013
MathSciNet review: 3080165
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Abstract: For several congruence subgroups of low levels and their conjugates, we derive differential equations satisfied by the Eisenstein series of weight 4 and relate them to elliptic curves whose associated newforms of weight 2 constitute the list of Martin and Ono of newforms given by eta-products/quotients.


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Additional Information

Masanobu Kaneko
Affiliation: Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
Email: mkaneko@math.kyushu-u.ac.jp

Yuichi Sakai
Affiliation: International Institute for Carbon-Neutral Energy Research, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
Address at time of publication: Yokomizo 3012-2, Ooki-machi, Mizunuma-gun, Fukuoka 830-0405, Japan
Email: dynamixaxs@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11917-9
Received by editor(s): January 3, 2012
Published electronically: June 26, 2013
Communicated by: Ken Ono
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.