Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms

This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range or illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience.The book is intended for researchers and graduate students in number theory.

Introduction.- Formal power series and pseudodifferential operators.- Jacobi-like forms and pseudodifferential operators.- Hecke operators.- Lie algebras.- Heat operators.- Group cohomology.- Quasimodular forms.- Quasimodular and modular polynomials.- Liftings of quasimodular forms.- Quasimodular forms and vector-valued modular forms.- Differential operators on modular forms.- Half-integral weight forms.- Projective structures.- Applications of quasimodular forms.