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Proceedings of the American Mathematical Society

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Divisibility of an eigenform by an eigenform


Authors: Jeffrey Beyerl, Kevin James and Hui Xue
Journal: Proc. Amer. Math. Soc. 142 (2014), 29-38
MSC (2010): Primary 11F11, 11F67
DOI: https://doi.org/10.1090/S0002-9939-2013-11840-X
Published electronically: September 10, 2013
MathSciNet review: 3119178
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Abstract: It has been shown in several settings that the product of two eigenforms is rarely an eigenform. In this paper we consider the more general question of when the product of an eigenform with any modular form is again an eigenform. We prove that this can occur only in very special situations. We then relate the divisibility of eigenforms to linear independence of vectors of Rankin-Selberg $ L$-values.


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Additional Information

Jeffrey Beyerl
Affiliation: Department of Mathematical Sciences, Clemson University, Box 340975, Clemson, South Carolina 29634-0975
Email: jbeyerl@clemson.edu

Kevin James
Affiliation: Department of Mathematical Sciences, Clemson University, Box 340975, Clemson, South Carolina 29634-0975
Email: kevja@clemson.edu

Hui Xue
Affiliation: Department of Mathematical Sciences, Clemson University, Box 340975, Clemson, South Carolina 29634-0975
Email: huixue@clemson.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11840-X
Received by editor(s): August 17, 2011
Received by editor(s) in revised form: February 23, 2012
Published electronically: September 10, 2013
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2013 By the authors