Hilbert Modular Forms

1990
ISBN: 978-3-540-50586-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 252 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1220 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Freitag, Eberhard

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.