Intro; Preface; Contents; Sturm-Like Bound for Square-Free Fourier Coefficients; 1 Introduction; 2 Proof of the Main Result; 2.1 Remarks; 2.2 Further Questions; References; Images of Maass-Poincaré Series in the Lower Half-Plane; 1 Introduction and Statement of Results; 2 Preliminaries; 2.1 Harmonic Maass Forms; 2.2 Poincaré Series; 3 Proof of Theorem 1.1; 3.1 The Holomorphic Part; 3.2 The Non-holomorphic Part; References; On Denominators of Values of Certain L-Functions When Twisted by Characters; 1 Introduction; 2 Preliminaries; 2.1 General Notation; 2.2 Siegel Modular Forms

2.3 Eisenstein Series2.4 Petersson Product; 2.5 Hecke Operators and L-Functions; 3 The Main Construction; 3.1 The Construction of gnk,ν(Ï#x87;); First Step: Exterior Twist; Second Step: Differential Operators; Third Step: Spectral Decomposition; 3.2 Forth Step: Level Change; Fifth Step: Normalization; 4 Congruence Primes and Denominators; 5 Congruences for Modular Forms; 6 Denominators Again; 7 Outlook; References; First Order p-Adic Deformations of Weight One Newforms; Introduction; Part A: The Regular Setting; 1 The General Case; 2 CM Forms; 2.1 The Case Where p Splits in K

2.2 The Case Where p Is Inert in K2.3 Numerical Examples; 3 RM Forms; Part B: The Irregular Setting; 4 Generalised Eigenspaces; 5 The General Case; 6 CM Forms; 7 RM Forms; References; Computing Invariants of the Weil Representation; 1 Introduction; 2 Finite Quadratic Modules and Weil Representations; 3 Invariants; 4 The Algorithm; 5 Reduction Mod; 6 Tables; References; The Metaplectic Tensor Product as an Instance of Langlands Functoriality; 1 Kazhdan-Patterson Coverings and Metaplectic Tensor Product; 1.1 Kazhdan-Patterson Covering; 1.2 Covers of Levi Subgroups

1.3 Metaplectic Tensor Product2 L-Group Formalism; 2.1 Dual Group; 2.2 Structural Facts; 2.3 L-Group and LLC; 2.4 Desiderata; 2.5 LLC for Covering Tori; 2.6 LLC for Principal Series; 2.7 Distinguished Splittings; 3 L-Group Interpretation of Metaplectic Tensor Product; 3.1 Setup; 3.2 The Conjecture; 3.3 Case of Principal Series; References; On Scattering Constants of Congruence Subgroups; 1 Introduction; 1.1 Scattering Constants; 1.2 Purpose of this Article; 1.3 Outline of the Article; 2 Background Material; 2.1 Congruence Subgroups; 2.2 Cusps; 2.3 Non-holomorphic Eisenstein Series

2.4 Scattering Functions and Scattering Constants3 The Principal Congruence Subgroup; 3.1 Cusps; 3.2 Scattering Functions; 4 Relation for Non-holomorphic Eisenstein Series; 5 Formulas for Scattering Constants; 6 Examples; References; The Bruinierâ#x80;#x93;Funke Pairing and the Orthogonal Complement of Unary Theta Functions; 1 Introduction; 2 Preliminaries; 2.1 Basic Definitions; 2.2 Half-Integral Weight Forms; 2.3 Theta Functions for Quadratic Polynomials; 3 The Bruinierâ#x80;#x93;Funke Pairing; 4 An Application to Lattice Theory; 4.1 An Application; 4.2 An Individual Case; References