Divisibility of an eigenform by an eigenform
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- by Jeffrey Beyerl, Kevin James and Hui Xue PDF
- Proc. Amer. Math. Soc. 142 (2014), 29-38
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.References
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
- MR Author ID: 629241
- Email: kevja@clemson.edu
- Hui Xue
- Affiliation: Department of Mathematical Sciences, Clemson University, Box 340975, Clemson, South Carolina 29634-0975
- Email: huixue@clemson.edu
- 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
- © Copyright 2013 By the authors
- 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
- MathSciNet review: 3119178