$T \overline{T}$-deformed modular forms

Certain objects of conformal field theory, for example partition functions on the rectangle and torus, one-point are either invariant or transform simply under modular group, properties which should be preserved $T\overline T$ deformation. The formulation proof this statement in fact extents to more general such as deformed Jacobi forms. We show that deformation acts their Mellin transform, multiplying it by a universal entire function. Finally we Maass forms torus eigenfunctions