Hecke Operators on Jacobi-like Forms

http://dx.doi.org/10.4153/CMB-2001-028-6
Canad. Math. Bull. 44(2001), 282-291

  Published:2001-09-01
 Printed: Sep 2001

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.