Related papers: Pullbacks of hermitian Maass lifts

While several instances of shifted convolution problems for GL(3) x GL(2) have been solved, the case where one factor is the classical divisor function and one factor is a GL(3) Fourier coefficient has remained open. We solve this case in…

We study a certain theta lift which maps weight $-2k$ to weight $1/2-k$ harmonic weak Maass forms for $k \in \mathbb{Z}, k \geq 0$, and which is closely related to the classical Shintani lift from weight $2k+2$ to weight $k+3/2$ cusp forms.…

We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary…

In this paper we give a formula for the central value of the completed $L$-function $L(s,Sym^{2} g\times f)$, where $f$ and $g$ are Hilbert newforms, by explicitly computing the local integrals appearing in the refined Gan-Gross-Prasad…

The $h$-deformation of functions on the Grassmann matrix group $Gr(2)$ is presented via a contraction of $Gr_q(2)$. As an interesting point, we have seen that, in the case of the $h$-deformation, both R-matrices of $GL_h(2)$ and $Gr_h(2)$…

We develop a (largely conjectural) theory of p-adic L-functions interpolating square roots of central L-values for automorphic forms on GSp(4) x GL(2) x GL(2), and a relation between these p-adic L-functions and families of Galois…

We provide transformation matrices for arbitrary Lorentz transformations of multidimensional Hermite functions in any dimension. These serve as a valuable tool for analyzing spacetime properties of MHS fields, and aid in the description of…

For any holomorphic mapping $f\colon X\to Y$ between a complex manifold $X$ and a complex Hermitian manifold $Y$ we extend the pullback $f^*$ from smooth forms to a class of currents. We provide a basic calculus for this pullback and show…

Some generalizations of the Maass relation for Siegel modular forms of higher degrees have been obtained by several authors. In the present article we first give a new generalization of the Maass relation for Siegel-Eisenstein series of…

We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and…

We prove the asymptotic formulae for several moments of derivatives of GL(2) L-functions over quadratic twists. The family of L-functions we consider has root number fixed to -1 and odd orthogonal symmetry. Assuming GRH we prove the…

Automorphic distributions for SL(2) arise as boundary values of modular forms and, in a more subtle manner, from Maass forms. In the case of modular forms of weight one or of Maass forms, the automorphic distributions have continuous first…

Suppose $\pi_1$ and $\pi_2$ are two Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$ such that for all primitive character $\chi$ we have $$ L(\tfrac{1}{2},\pi_1\otimes\chi)=L(\tfrac{1}{2},\pi_2\otimes\chi). $$ Then we show that $\pi_1=\pi_2$.

In our previous papers \cite{doz1,doz2} we studied Laguerre functions and polynomials on symmetric cones $\Omega=H/L$. The Laguerre functions $\ell^{\nu}_{\mathbf{n}}$, $\mathbf{n}\in\mathbf{\Lambda}$, form an orthogonal basis in…

We establish the existence of the symmetric power liftings of all holomorphic Hecke eigenforms.

In our previous publications we have introduced analogs of partial derivatives on the algebras U(gl(N)). In the present paper we compare two methods of introducing these analogs: via the so-called quantum doubles and by means of a…

In studies of smooth maps with good differential topological conditions such as immersions, embeddings, Morse functions and their higher dimensional versions including fold maps and application to geometry, especially algebraic and…

In this paper, we use regularized theta liftings to construct weak Maass forms weight 1/2 as lifts of weak Maass forms of weight 0. As a special case we give a new proof of some of recent results of Duke, Toth and Imamoglu on cycle…

In a previous paper we have introduced matrix-valued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2)\times SU(2). In particular the matrix-size of the polynomials is arbitrarily large. The…

In this paper we define the notion of pullback lifting of a lifting crossed module over a crossed module morphism and interpret this notion in the category of group-groupoid actions as pullback action. Moreover, we give a criterion for the…