This monograph introduces two approaches to studying Siegel modular forms: the classical
approach as holomorphic functions on the Siegel upper half space and the approach via
representation theory on the symplectic group. By illustrating the interconnections shared by
the two this book fills an important gap in the existing literature on modular forms. It
begins by establishing the basics of the classical theory of Siegel modular forms and then
details more advanced topics. After this much of the basic local representation theory is
presented. Exercises are featured heavily throughout the volume the solutions of which are
helpfully provided in an appendix. Other topics considered include Hecke theory Fourier
coefficients cuspidal automorphic representations Bessel models and integral representation.
Graduate students and young researchers will find this volume particularly useful. It will also
appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is
recommended but there are a number of appendices included if the reader is not already
familiar.
