Related papers: Kohnen's limit process for real-analytic Siegel mo…

We find automorphic form corrections which are generalized Lorentzian Kac--Moody superalgebras without odd real simple roots (see R. Borcherds \cite{Bo1} -- \cite{Bo7}, V. Kac \cite{Ka1} -- \cite{Ka3}, R. Moody \cite{Mo} and \S~6 of this…

In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology,…

This is an ultimate completion of our earlier paper [Acta.\ Math.\ Hungar.\ 140 (2013), 248--292] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were…

In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of…

We prove bounds of the form $\sum_{e\in I\cap\sigma_\di (H)} \dist (e,\sigma_\e (H))^{1/2} \leq L^1$-norm of a perturbation, where $I$ is a gap. Included are gaps in continuum one-dimensional periodic Schr\"odinger operators and finite gap…

In this paper, we define the concept of Jacobi forms of half-integral weight using Takase's automorohic factor of weight 1/2 for a two-fold covering group of the symplectic group on the Siegel upper half plane and find covariant maps for…

We consider some questions related to the signs of Hecke eigenvalues or Fourier coefficients of classical modular forms. One problem is to determine to what extent those signs, for suitable sets of primes, determine uniquely the modular…

We establish the existence of complete K\"ahler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane…

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…

A Lemma of Riemann--Lebesgue type for Fourier--Jacobi coefficients is derived. Via integral representations of Dirichlet--Mehler type for Jacobi polynomials its proof directly reduces to the classical Riemann--Lebesgue Lemma for Fourier…

We study the meromorphic modular forms defined as sums of -k (k>1) powers of integral quadratic polynomials with negative discriminant. These functions can be viewed as meromorphic analogues of the holomorphic modular forms defined in the…

We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other…

We investigate Poincar\'e series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms…

We give a geometric derivation of Schottky's equation in genus four for the period matrices of Riemann surfaces among all period matrices. The equation arises naturally from the singularity theory of the Gauss map on the theta divisor, and…

In this work we prove a prime number type theorem involving the normalised Fourier coefficients of holomorphic and Maass cusp forms, using the classical circle method. A key point is in a recent paper of Fouvry and Ganguly, based on…

This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into…

We discuss mock automorphic forms from the point of view of representation theory, that is, obtained from weak harmonic Maass forms give rise to nontrivial $(\mathfrak{g},K)$-cohomology. We consider the possibility of replacing the…

We define and compute a cohomology of the space of Jacobi forms based on precise analogues of Zhu reduction formulas. A counterpart of the Bott-Segal theorem for the reduction cohomology of Jacobi forms on the torus is proven. It is shown…

We investigate so-called "higher" Siegel theta lifts on Lorentzian lattices in the spirit of Bruinier-Ehlen-Yang and Bruinier-Schwagenscheidt. We give a series representation of the lift in terms of Gauss hypergeometric functions, and…