Operator-Mediated Completion Theory for Nonclassical Automorphic Objects
Operator-Mediated Completion Theory for Nonclassical Automorphic Objects Research-Monograph TOC PART I — THE AUTOMORPHIC CLOSURE PROBLEM Chapter 1. Classical Automorphic Closure 1.1 Group actions and slash operators 1.2 Weight, multiplier, and representation 1.3 Exact transformation laws 1.4 Holomorphic modular forms 1.5 Meromorphic modular forms 1.6 Jacobi transformation laws 1.7 Maass and real-analytic automorphic objects 1.8 Boundary and cusp behavior 1.9 Closure as an exact structural condition 1.10 Classical modularity as the zero-defect case Chapter 2. Nonclassical Automorphic Objects 2.1 Holomorphic objects failing exact modular closure 2.2 Mock modular forms 2.3 False theta and false modular structures 2.4 Partial theta structures 2.5 Quantum modular forms 2.6 Harmonic Maass forms 2.7 Maass–Jacobi and harmonic Maass–Jacobi forms 2.8 Appell–Lerch structures 2.9 Indefinite theta functions 2.10 Eisenstein-type nonholomorphic completions 2.11 Mixed modular structures 2.12 Why...