Related papers: Pointwise Properties of Fourier-Jacobi-Forms
We give conditions under which a self-dual holomorphic cusp form is determined up to scalar multiplication by the signs of its Fourier coefficients.
We combine the Duke-Imamoglu-Ikeda lifting with the theta lifting to produce new CAP representations of metaplectic, symplectic and orthogonal groups. These constructions partially generalize the theories of Waldspurger on the Shimura…
This article is a study on the summability of random Fourier--Jacobi series of some functions in different spaces. We consider the random series $ \sum_{n=0}^\infty a_nA_n(\omega)p_n^{(\gamma,\delta)}(y), $ where…
Aim of this article is a Satake type theorem for super automorphic forms on a complex bounded symmetric super domain B of rank 1 with respect to a lattice. This theorem - roughly speaking - says that for large weight k and all p from 1 to…
In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp…
In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke…
In this work we study the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms of higher index, generalizing previous results of Arakawa and Murase. Furthermore, we obtain algebraicity results on special…
This article is an overview of Zagier's and Kim's work on traces of singular moduli. We give more detailed or new proofs to some of their results and also describe some algorithms to compute spaces of Jacobi forms and weight $3/2$ modular…
Kaneko's formula expresses the Fourier coefficients of the elliptic modular $j$-function as finite sums of singular moduli. First published as a short article in 1996, it was presented as a consequence of Zagier's work inspired by Borcherds…
Following Zagier, this work studies the rationality and divisibility of Fourier coefficients of meromorphic Hilbert modular forms associated with real quadratic fields, using theta lifts and weak Maass forms. We establish conditions where…
The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy's largest root test in…
We develop vanishing and cuspidality criteria for quaternionic modular forms on $G=\mathrm{Spin}(4,4)$ using a theory of scalar Fourier coefficients. By analyzing a Fourier-Jacobi expansion for these forms, we prove that a level one…
In this paper we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann-Liouville fractional integral and derivative operators on a compact of the real axis.This approach has some advantages and allows us to…
We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi-Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows…
We calculate the $k$-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for $k=1$ to derive a closed-form expression for eigenvalue density. For real matrices we…
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.…
In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody…
The family of circular Jacobi $\beta$ ensembles has a singularity of a type associated with Fisher and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of the corresponding bulk scaled spectral…
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…
Borcherds-Zagier bases of the spaces of weakly holomorphic modular forms of weights 1/2 and 3/2 share the Fourier coefficients which are traces of singular moduli. Recently, Duke, Imamo\={g}lu, and T\'{o}th have constructed a basis of the…