Alladi Ramakrishnan Hall

Converse theorem for quasimodular forms

Mrityunjoy Charan

IMSc

A converse theorem in the theory of automorphic forms establishes a correspondence between the functions that
satisfy certain transformation properties, on one hand, and Dirichlet series satisfying certain analytic properties, on the
other hand. For example, the well-known Hecke’s converse theorem establishes an
equivalence between modular forms on $SL_2(Z)$ and Dirichlet series satisfying a certain functional equation,
meromorphic continuation, and boundedness in the vertical strips. A very significant and useful generalization of Hecke’s
converse theorem to congruence subgroups $Gamma_0(N)$ was done by Weil. In this talk, we discuss converse theorem for
quasimodular forms.