Related papers: On the lifting of Hilbert cusp forms to Hilbert-Si…

We give a derivative version of the relative trace formula on PGL(2) studied in our previous work, and obtain a formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we…

We construct one parameter families of overconvergent Siegel-Hilbert modular forms. In particular, for any classical Siegel-Hilbert modular eigenform one can find a rigid analytic disc centered at this point, on which an infinite family of…

Let $\frak T_2$ (resp. $\mathfrak{T}$) be the Hermitian symmetric domain of $Spin(2,10)$ (resp. $E_{7,3}$). In the previous work, we constructed holomorphic cusp forms on $\mathfrak{T}$ from elliptic cusp forms with respect to…

Let $F$ and $G$ be Siegel cusp forms for $\Sp_4(\Z)$ and weights $k_1, k_2$ respectively. Also let $F$ and $G$ be Hecke eigenforms lying in distinct eigen spaces. Further suppose that neither $F$ nor $G$ is a Saito-Kurokawa lift. In this…

We give a summary of results for dimensions of spaces of cuspidal Siegel modular forms of degree 2. These results together with a list of dimensions of the irreducible representations of the finite groups GSp(4,Fp) are then used to produce…

We compute the space $S_2(K(N))$ of weight $2$ Siegel paramodular cusp forms of squarefree level $N<300$. In conformance with the paramodular conjecture of A. Brumer and K. Kramer, the space is only the additive (Gritsenko) lift space of…

We prove an upper bound for the L^4-norm and for the L^2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form of large weight. The method is based on Watson's formula and estimating a mean value of certain L-functions…

In this article we show analytic properties of certain Rankin-Selberg type Dirichlet series for holomorphic Jacobi cusp forms of integral weight and of half-integral weight. The numerators of these Dirichlet series are the inner products of…

The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of Saito-Kurokawa type, in which case the degree 4 spinor L-function L(s, F) is…

The aim of this paper is to carry out an explicit construction of CAP representations of GL(2) over a division quaternion algebra with discriminant two. We first construct cusp forms on such group explicitly by lifting from Maass cusp forms…

Cusp forms are certain holomorphic functions defined on the upper half-plane, and the space of cusp forms for the principal congruence subgroup $\Gamma(p)$, $p$ a prime, is acted by $\mathrm{SL}_2(\mathbb{F}_p)$. Meanwhile, there is a…

The purpose of this paper is to collect and make explicit the results of Gel'fand, Graev and Piatetski-Shapiro and Miyazaki for the $GL(3)$ cusp forms which are non-trivial on $SO(3,\mathbb{R})$. We give new descriptions of the spaces of…

This paper gives a simple method for constructing vector-valued Siegel modular forms from scalar-valued ones. The method is efficient in producing the siblings of Delta, the smallest weight cusp forms that appear in low degrees. It also…

In this paper we generalize a well-known isomorphism between the space of cusp forms of weight $k$ for a Fuchsian subgroup of the first kind $\Gamma \subset\mathrm{SL}_{2}(\mathbb{R})$ and the space of certain Maa{\ss} forms of weight $k$…

We introduce extensions of the multidimensional Heisenberg group $\mathbb{H}^n$ by two-parameter groups of dilations, and then classify the extended groups up to isomorphism, by employing Lie algebra techniques. We show that the groups are…

In this article we obtain an explicit formula for certain Rankin-Selberg type Dirichlet series associated to certain Siegel cusp forms of half-integral weight. Here these Siegel cusp forms of half-integral weight are obtained from the…

In this paper, we prove the existence of certain lifts of Hilbert cusp forms to general odd spin groups. We then use those lifts to provide evidence for a conjecture of Gross on the modularity of abelian varieties not of ${\rm GL}_2$-type.

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

We find the average value of the $L^4$-norm of holomorphic Hecke cusp forms of weight within a dyadic interval, up to an error which saves a power of the weight.

An AF-algebra is assigned to each cusp form f of weight two; we study properties of this operator algebra, when f is a Hecke eigenform.