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Hecke Operators on Jacobi-like Forms

Open Access article
 Printed: Sep 2001
  • Min Ho Lee
  • Hyo Chul Myung
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Jacobi-like forms for a discrete subgroup $\G \subset \SL(2,\mbb R)$ are formal power series with coefficients in the space of functions on the Poincar\'e 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.
MSC Classifications: 11F25, 11F12 show english descriptions Hecke-Petersson operators, differential operators (one variable)
Automorphic forms, one variable
11F25 - Hecke-Petersson operators, differential operators (one variable)
11F12 - Automorphic forms, one variable

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