Abstract
One of the effective tools in the theory of modular forms is the notion of Hecke operators (see e.g. [85]). Hecke operators can also be considered in connection with various other topics which involve actions of a discrete subgroup of a semisimple Lie group. In this chapter we introduce Hecke operators acting on the spaces of Jacobi-like forms, modular series, and pseudodifferential operators. We show that these Hecke operator actions are compatible with the mutual correspondences among those three objects studied in Chapter 1. We also discuss connections of these actions with Hecke operator actions on certain types of linear ordinary differential equations.
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Choie, Y., Lee, M. (2019). Hecke Operators. In: Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-29123-5_3
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DOI: https://doi.org/10.1007/978-3-030-29123-5_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29122-8
Online ISBN: 978-3-030-29123-5
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