Related papers: Massive deformations of Maass forms and Jacobi for…
We initiate the study of generalized Maass wave forms, those Maass wave forms for which the multiplier system is not necessarily unitary. We then prove some basic theorems inherited from the classical theory of modular forms with a…
We use Poincare series for massive Maass-Jacobi forms to define a "massive theta lift", and apply it to the examples of the constant function and the modular invariant j-function, with the Siegel-Narain theta function as integration kernel.…
Recently Bringmann, Raum and Richter generalised the definition of Jacobi forms and Skoruppa's skew-holomorphic Jacobi forms by intertwining with harmonic Maass forms. We prove the isomorphism of the Kohnen's plus space analogue of harmonic…
We construct harmonic weak Maass forms that map to cusp forms of weight $k\geq 2$ with rational coefficients under the $\xi$-operator. This generalizes work of the first author, Griffin, Ono, and Rolen, who constructed distinguished…
In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.
We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear…
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…
Certain objects of conformal field theory, for example partition functions on the rectangle and the torus, and one-point functions on the torus, are either invariant or transform simply under the modular group, properties which should be…
Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of…
In earlier papers on the loop variable approach to gauge invariant interactions in string theory, a ``wave functional'' with some specific properties was invoked. It had the purpose of converting the generalized momenta to space time…
The Minkowski question mark function is a rich object which can be explored from the perspective of dynamical systems, complex dynamics, metric number theory, multifractal analysis, transfer operators, integral transforms, and as a function…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting them to the Ramanujan Mock Theta functions and to the cusp forms generated from the…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the index is allowed to be a complex number instead of a non-negative integer. These functions are referred to…
We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact…
We construct an infinite set of conserved tensor currents of rank $2n$, $n=1,2,\dots$, in the two-dimensional theory of free massive fermions, which are bilinear in the fermionic fields. The one-point functions of these currents on the…
Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.
Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker--Eisenstein…
We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface $S$ under deformation of the surface. Our calculations indicate that if…