"The Theory of Jacobi Forms" is a book edited by J. Coates and S. Helgason, published by Springer Science+Business Media, LLC in 1985. The book is authored by Martin Eichler and Don Zagier. Martin Eichler is based in Arlesheim, Switzerland, while Don Zagier is a professor at the University of Maryland, USA. The book is part of the "Progress in Mathematics" series, volume 55. It covers the theory of Jacobi forms, which are a type of modular form with additional variables. The book is structured into three main parts: basic properties, relations with other types of modular forms, and the ring of Jacobi forms. It includes topics such as Jacobi forms and the Jacobi group, Eisenstein series, cusp forms, Taylor expansions, Hecke operators, and connections with modular forms of half-integral weight. The book also discusses Fourier-Jacobi expansions, Jacobi theta series, and the Saito-Kurokawa conjecture. It provides an explicit description of the space of Jacobi forms, examples of Jacobi forms of index greater than 1, and discusses the dimension formula for Jacobi forms. The book includes tables, a bibliography, and is a comprehensive resource on the theory of Jacobi forms. It is intended for mathematicians and researchers in the field of number theory and modular forms. The book is published with ISBN numbers and is available in both print and electronic formats. The copyright is held by Springer Science+Business Media New York, and the original publication was by Birkhäuser Boston, Inc in 1985. The book has an introduction, notations, and various chapters that provide a detailed exploration of Jacobi forms and their properties."The Theory of Jacobi Forms" is a book edited by J. Coates and S. Helgason, published by Springer Science+Business Media, LLC in 1985. The book is authored by Martin Eichler and Don Zagier. Martin Eichler is based in Arlesheim, Switzerland, while Don Zagier is a professor at the University of Maryland, USA. The book is part of the "Progress in Mathematics" series, volume 55. It covers the theory of Jacobi forms, which are a type of modular form with additional variables. The book is structured into three main parts: basic properties, relations with other types of modular forms, and the ring of Jacobi forms. It includes topics such as Jacobi forms and the Jacobi group, Eisenstein series, cusp forms, Taylor expansions, Hecke operators, and connections with modular forms of half-integral weight. The book also discusses Fourier-Jacobi expansions, Jacobi theta series, and the Saito-Kurokawa conjecture. It provides an explicit description of the space of Jacobi forms, examples of Jacobi forms of index greater than 1, and discusses the dimension formula for Jacobi forms. The book includes tables, a bibliography, and is a comprehensive resource on the theory of Jacobi forms. It is intended for mathematicians and researchers in the field of number theory and modular forms. The book is published with ISBN numbers and is available in both print and electronic formats. The copyright is held by Springer Science+Business Media New York, and the original publication was by Birkhäuser Boston, Inc in 1985. The book has an introduction, notations, and various chapters that provide a detailed exploration of Jacobi forms and their properties.