Hilbert Modular Forms

by Eberhard Freitag

Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded in giving proofs which are both elementary and complete. The book contains an introduction to Hilbert modular forms, reduction theory, the trace formula and Shimizu's formulae, the work of Matsushima and Shimura, analytic continuation of Eisenstein series, the cohomology and its Hodge decomposition. Basic facts about algebraic numbers, integration, alternating differential forms and Hodge theory are included in convenient appendices so that the book can be used by students with a knowledge of complex analysis (one variable) and algebra.

260 pages, Paperback

First published May 10, 1990

Reviews

[Wissam Raji · Rating 4 out of 5]

An excellent book on the theory of Hilbert modular forms. Very easy introduction to the theory with a nice appendix of basic algebraic number theory definitions. Highly recommended for those who want to learn about HMF.