Hilbert Modular Forms / Edition 1

by Eberhard Freitag

Overview

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.

Product Details

ISBN-13:	9783642080722
Publisher:	Springer Berlin Heidelberg
Publication date:	12/08/2010
Edition description:	1990
Pages:	252
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

I. Hilbert Modular Forms.- II. Dimension Formulae.- III. The Cohomology of the Hilbert Modular Group.- Appendices.- I. Algebraic Numbers.- II. Integration.- III. Alternating Differential Forms.

Editorial Reviews

A pretty little monograph, the brevity and elegant depth of which would make it suitable as a focus for the work of (say) a graduate seminar. Though some historical and motivational material is included, the author--evidently convinced that his story will tell itself--has provided probably too little such support to permit his book to serve well the advanced undergraduates he had in mind when he wrote the appendices. Nicely produced. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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