Related papers: Period functions for Maass wave forms. I

For a fixed SL(3, Z) Maass form g, we consider the family of L-functions L(g \times u_j, s) where u_j runs over the family of Hecke-Maass cusp forms on SL(2,Z). We obtain an estimate for the second moment of this family of L-functions at…

Let K be an imaginary quadratic field of discriminant -D_K<0. We introduce a notion of an adelic Maass space S_{k, -k/2}^M for automorphic forms on the quasi-split unitary group U(2,2) associated with K and prove that it is stable under the…

The modular group $\operatorname{PSL}_2(\mathbb{Z})$ acts on the upper-half plane $\mathbb{HP}$ with quotient the modular orbifold, uniformized by the function $\mathfrak{j} \colon \mathbb{HP}\to \mathbb{C}$. We first show that second…

Modular graph functions associate to a graph an $SL(2,Z)$-invariant function on the upper half plane. We obtain the Fourier series of modular graph functions of arbitrary weight $w$ and two-loop order. The motivation for this work is to…

We study the vector space V_k^m(\lambda) of shifted polyharmonic Maass forms of weight k \in 2Z, depth m \geq 0, and shift \lambda \in C. This space is composed of real-analytic modular forms of weight k for PSL(2,Z) with moderate growth at…

We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…

Let $(M,g)$ be a $n-$dimensional, compact Riemannian manifold. We define the frequency scale $\lambda$ of a function $f \in C^{0}(M)$ as the largest number such that $\left\langle f, \phi_k \right\rangle =0$ for all Laplacian eigenfunctions…

Let $0<\alpha<2$, $\beta>0$ and $\alpha/2<|s|\leq 1$. In a previous work, we obtained all possible values of the Lebesgue exponent $p=p(\gamma)$ for which the Fourier transform of $ E_{\alpha,\beta}(e^{\dot{\imath}\pi s} |\cdot|^{\gamma} )$…

We consider the $SL(2,R)$ action on moduli spaces of quadratic differentials. If $\mu$ is an $SL(2,R)$-invariant probability measure, crucial information about the associated representation on $L^2(\mu)$ (and in particular, fine asymptotics…

Let E_lambda be a Hilbert space, whose elements are functions spanned by the eigenfunctions of the Laplace-Beltrami operator associated with an eigenvalue lambda>0. The norm of elements in this space is given by the Petersson inner product.…

We initiate the study of generalized Maass wave forms, those Maass wave forms for which the multiplier system is not necessarily unitary. We then prove some basic theorems inherited from the classical theory of modular forms with a…

The study of the evolution of a suprathermal electron beam traveling through a background plasma is relevant for the physics of solar flares and their associated type III solar radio bursts. As they evolve guided by the coronal magnetic…

Spectra of the neutral heavy mesons, $\eta_c(1S,2S)$, $J/\psi$, $\psi(2S)$, $\eta_b(1S,2S,3S)$, $\Upsilon(1S,2S,3S)$, $D$, $D^\ast$, $B$, $B^\ast$, $B_s$ and $B_s^\ast$, in a homogeneous magnetic field are analyzed in a potential model of…

False theta functions form a family of functions with intriguing modular properties and connections to mock modular forms. In this paper, we take the first step towards investigating modular transformations of higher rank false theta…

For every positive integral level $k$ we study arithmetic properties of certain holomorphic modular forms associated to modular invariant spaces spanned by graded dimensions of $L_{\hat{sl_2}}(k \Lambda_0)$-modules. We found a necessary and…

Spherical wave functions play an important role in the theoretical study of antenna. When they are used to investigate the stored energy outside the circumscribing sphere of the antenna, two different types of modal quality factors appear…

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…

We investigate the meromorphic quasi-modular forms and their $L$-functions. We study the space of meromorphic quasi-modular forms. Then we define their $L$-functions by using the technique of regularized integral. Moreover, we give an…

We consider a magnetic Laplacian with periodic magnetic potentials on periodic discrete graphs. Its spectrum consists of a finite number of bands, where degenerate bands are eigenvalues of infinite multiplicity. We obtain a specific…

Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained. They are defined as eigenfunctions of the differential Casimir operators for the…