Related papers: Generalized Maass Wave Forms
The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group PSL(2,Z) with general multiplier systems and real weight. A selection of numerical results obtained with these…
We define one-parameter "massive" deformations of Maass forms and Jacobi forms. This is inspired by descriptions of plane gravitational waves in string theory. Examples include massive Green's functions (that we write in terms of…
The theory for large amplitude circularly polarized waves propagating along an external magnetic field is extended in order to include also vacuum polarization effects. A general dispersion relation, which unites previous results, is…
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…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting them to the Ramanujan Mock Theta functions and to the cusp forms generated from the…
We consider (generalized) periods of Maass forms along non-closed geodesics having a closed geodesic as the limit set.
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport…
Considered herein are a number of variants of the Boussinesq type systems modeling surface water waves. Such equations were derived by different authors to describe the two-way propagation of long gravity waves. A question of existence of…
Complete analysis of quantum wave functions of linear systems in an arbitrary number of dimensions is given. It is shown how one can construct a complete set of stationary quantum states of an arbitrary linear system from purely classical…
We discuss gravitational waves from merging binaries using a Newtonian approach with some inputs from the Post-Newtonian formalism. We show that it is possible to understand the key features of the signal using fundamental physics and also…
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
First, we obtain the plane wave solution of the linearized massive conformal gravity field equations. It is shown that the theory has seven physical plane waves. In addition, we investigate the gravitational radiation from binary systems in…
This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The problem of interbasis expansions of the wavefunctions is completely…
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…
For steady-state and some other types of mechanical waves of an arbitrary form, intensity and nature, propagating in a free uniform waveguide, we present the following. Relations for the axial momentum as it directly follows from the…
We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of…