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April, 2018 Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality
Seokho Jin, Jongryul Lim, Subong Lim
Taiwanese J. Math. 22(2): 301-311 (April, 2018). DOI: 10.11650/tjm/170811


In this paper, we prove that if the Fourier coefficients of a vector-valued modular form satisfy the Hecke bound, then it is cuspidal. Furthermore, we obtain an analogous result with regard to Jacobi forms by applying an isomorphism between vector-valued modular forms and Jacobi forms. As an application, we prove a result on the growth of the number of representations of $m$ by a positive definite quadratic form $Q$.


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Seokho Jin. Jongryul Lim. Subong Lim. "Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality." Taiwanese J. Math. 22 (2) 301 - 311, April, 2018.


Received: 2 January 2017; Revised: 7 July 2017; Accepted: 28 August 2017; Published: April, 2018
First available in Project Euclid: 4 October 2017

zbMATH: 06965371
MathSciNet: MR3780718
Digital Object Identifier: 10.11650/tjm/170811

Primary: 11F30 , 11F50

Keywords: Hecke bound , jacobi forms , vector-valued modular forms

Rights: Copyright © 2018 The Mathematical Society of the Republic of China


Vol.22 • No. 2 • April, 2018
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