#### 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.

Done