Related papers: Fourier-Jacobi expansion of automorphic forms gene…

This paper is third in a series of three, following "Summation Formulas, from Poisson and Voronoi to the Present" (math.NT/0304187) and "Distributions and Analytic Continuation of Dirichlet Series" (math.FA/0403030). The first is primarily…

We prove general equidistribution statements (both conditional and unconditional) relating to the Fourier coefficients of arithmetically normalized holomorphic Hecke cusp forms $f_1,\ldots,f_k$ without complex multiplication, of equal…

We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we…

Let $f$ be a newform of even weight $2\kappa$ for $D^\times$, where $D$ is a possibly split indefinite quaternion algebra over $\mathbb{Q}$. Let $K$ be a quadratic imaginary field splitting $D$ and $p$ an odd prime split in $K$. We extend…

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…

We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix…

We introduce a central extension of the preprojective algebra of a finite Dynkin quiver (depending on a regular weight for the corresponding root system), whose natural deformed version is flat (unlike that for the preprojective algebra).…

This paper generalises previous work of the author to the setting of overconvergent $p$-adic automorphic forms for a definite quaternion algebra over a totally real field. We prove results which are analogues of classical `level raising'…

We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over…

In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…

We provide a simple and new induction based treatment of the problem of distinguishing cusp forms from the growth of the Fourier coefficients of modular forms. Our approach gives the best possible ranges of the weights for this problem, and…

We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…

Let $G$ be a finite group and, for a given complex character $\chi$ of $G$, let ${\mathbb{Q}}(\chi)$ denote the field extension of ${\mathbb{Q}}$ obtained by adjoining all the values $\chi(g)$, for $g\in G$. The group $G$ is called…

We prove that the commutation relations among the generators of the quadratic Heisenberg algebra of dimension $n\in\mathbb{N}$, look like a kind of \textit{non-commutative extension} of $\hbox{sl}(2, \mathbb{C})$ (more precisely of its…

In the 2002 Durham Symposium, Markus Linckelmann [1] conjectured the existence of a regular central k*-extension of the full subcategory over the selfcentralizing Brauer pairs of the Frobenius P-category F_{(b,G)} associated with a block b…

We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…

Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of…

We consider new series expansions for variants of the so-termed ordinary geometric square series generating functions originally defined in the recent article titled "Square Series Generating Function Transformations" (arXiv: 1609.02803).…

We consider a Cauchy problem for some family of q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables t and z for given formal power series initial…

We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For…