Hilbert Modular Forms

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Hilbert Modular Surfaces

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Author : Gerard van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Hilbert Modular Surfaces written by Gerard van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.

Lectures On Hilbert Modular Varieties And Modular Forms

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Author : Eyal Zvi Goren
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Lectures On Hilbert Modular Varieties And Modular Forms written by Eyal Zvi Goren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This book is devoted to certain aspects of the theory of $p$-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of $p$-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelianvarieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of $p$-adic Hilbert modular forms and the geometry ofmoduli spaces of abelian varieties are related. This relation is used to study $q$-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-experts. It attempts to provide the necessary background to all concepts exposed in it. It may serve as a textbook for an advanced graduate course.

Hilbert Modular Forms

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Author : Eberhard Freitag
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Hilbert Modular Forms written by Eberhard Freitag and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

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.

Holomorphic Hilbert Modular Forms

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Author : Paul B. Garrett
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1989-09-01

Holomorphic Hilbert Modular Forms written by Paul B. Garrett and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-01 with Mathematics categories.

An introduction to a substantial part of the theory of holomorphic Hilbert modular forms, associated L-functions, and their arithmetic. As such, it is an introduction to the theory of automorphic forms in general, especially to the arithmetic of holomorphic forms. Annotation copyrighted by Book News, Inc., Portland, OR

Hilbert Modular Forms And Iwasawa Theory

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Author : Haruzo Hida
language : en
Publisher: Clarendon Press
Release Date : 2006-06-15

Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.

Hilbert Modular Forms Mod P And P Adic Aspects

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Author : Fabrizio Andreatta
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Hilbert Modular Forms Mod P And P Adic Aspects written by Fabrizio Andreatta and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.

Periods Of Hilbert Modular Surfaces

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Author : T. Oda
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Periods Of Hilbert Modular Surfaces written by T. Oda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Hilbert Modular Forms With Coefficients In Intersection Homology And Quadratic Base Change

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Author : Jayce Getz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-28

Hilbert Modular Forms With Coefficients In Intersection Homology And Quadratic Base Change written by Jayce Getz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-28 with Mathematics categories.

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Hilbert Modular Forms And Iwasawa Theory

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Author : Haruzo Hida
language : en
Publisher: Oxford University Press
Release Date : 2006-06-15

Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.

Describing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author.

On Hilbert Modular Forms

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Author : Hai Trung Dang Ho
language : en
Publisher:
Release Date : 2006

On Hilbert Modular Forms written by Hai Trung Dang Ho and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Hilbert modules categories.