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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.


References [Enhancements On Off] (What's this?)

  • 1. P. Guerzhoy, The Ramanujan differential operator, a certain CM elliptic curve and Kummer congruences, Compositio Mathematica, 141 (2005), no. 3, 583-590. MR 2135278 (2005m:11083)
  • 2. T. Honda and I. Miyawaki, Zeta-functions of elliptic curves of $ 2$-power conductor, J. Math. Soc. Japan, 26 (1974), no. 2, 362-373. MR 0360594 (50:13042)
  • 3. Y. Martin and K. Ono, Eta-quotients and elliptic curves, Proc. Amer. Math. Soc., 125 (1997), 3169-3176. MR 1401749 (97m:11057)

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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.

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