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Hecke Operators on Jacobi-like Forms

Published online by Cambridge University Press:  20 November 2018

Min Ho Lee  and
Hyo Chul Myung
Min Ho Lee
Affiliation:
Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614 USA, e-mail: [email protected]
Hyo Chul Myung
Affiliation:
Korea Institute for Advanced Study and KAIST 207-43 Chunryangri-dong Dongdaemoon-ku Seoul 130-012 Korea, e-mail: [email protected]
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Abstract

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Jacobi-like forms for a discrete subgroup $\Gamma \,\subset \,\text{SL}\left( 2,\,\mathbb{R} \right)$ are formal power series with coefficients in the space of functions on the Poincaré upper half plane satisfying a certain functional equation, and they correspond to sequences of certain modular forms. We introduce Hecke operators acting on the space of Jacobi-like forms and obtain an explicit formula for such an action in terms of modular forms. We also prove that those Hecke operator actions on Jacobi-like forms are compatible with the usual Hecke operator actions on modular forms.

Keywords

11F2511F12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 282 - 291
Copyright
Copyright © Canadian Mathematical Society 2001

References

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