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Author : T. Oda
Publisher : Springer Science & Business Media
Page : 141 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492019
Author : T. Oda
Publisher : Unknown
Page : 144 pages
File Size : 40,5 Mb
Release : 1982-01-01
Category : Electronic
ISBN : 1468492020
Author : Gerard van der Geer
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642615535
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.
Author : Friedrich Hirzebruch,Gerard van der Geer
Publisher : Unknown
Page : 200 pages
File Size : 48,7 Mb
Release : 1981
Category : Discontinuous groups
ISBN : UOM:39015015619466
Author : Jayce Getz,Mark Goresky
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 40,8 Mb
Release : 2012-03-28
Category : Mathematics
ISBN : 9783034803519
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.
Author : Jan Nagel,Chris Peters
Publisher : Cambridge University Press
Page : 293 pages
File Size : 49,7 Mb
Release : 2007-05-03
Category : Mathematics
ISBN : 9780521701747
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Author : Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Publisher : JHU Press
Page : 946 pages
File Size : 46,7 Mb
Release : 2004-03-11
Category : Mathematics
ISBN : 0801878608
In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.
Author : Benjamin Howard,Tonghai Yang
Publisher : Springer Science & Business Media
Page : 146 pages
File Size : 44,7 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9783642239786
This monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch-Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.
Author : Jean-Pierre Labesse,Joachim Schwermer
Publisher : Springer
Page : 358 pages
File Size : 55,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468769
Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.
Author : Atsushi Ichino,Kartik Prasanna
Publisher : American Mathematical Society
Page : 214 pages
File Size : 42,7 Mb
Release : 2021-02-23
Category : Mathematics
ISBN : 9781470448943
This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.
Author : Alexander Caspar
Publisher : Unknown
Page : 112 pages
File Size : 42,6 Mb
Release : 2003
Category : Hilbert modular surfaces
ISBN : UOM:39015058213821
Author : Baskar Balasubramanyam,Haruzo Hida,A Raghuram,Jacques Tilouine
Publisher : World Scientific
Page : 344 pages
File Size : 50,9 Mb
Release : 2016-06-14
Category : Mathematics
ISBN : 9789814719247
The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n). Contents:An Overview of Serre's p-Adic Modular Forms (Miljan Brakočević and R Sujatha)p-Adic Families of Ordinary Siegel Cusp Forms (Jacques Tilouine)Ordinary Families of Automorphic Forms on Definite Unitary Groups (Baskar Balasubramanyam and Dipramit Majumdar)Notes on Modularity Lifting in the Ordinary Case (David Geraghty)p-Adic L-Functions for Hilbert Modular Forms (Mladen Dimitrov)Arithmetic of Adjoint L-Values (Haruzo Hida)p-Adic L-Functions for GLn (Debargha Banerjee and A Raghuram)Non-Triviality of Generalised Heegner Cycles Over Anticyclotomic Towers: A Survey (Ashay A Burungale)The Euler System of Heegner Points and p-Adic L-Functions (Ming-Lun Hsieh)Non-Commutative q-Expansions (Mahesh Kakde) Readership: Researchers in algebra and number theory.
Author : Jan H. Bruinier
Publisher : Springer
Page : 156 pages
File Size : 46,5 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540458722
Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
Author : Friedrich Hirzebruch
Publisher : Unknown
Page : 108 pages
File Size : 44,5 Mb
Release : 1973
Category : Discontinuous groups
ISBN : STANFORD:36105031559730
Author : Eyal Zvi Goren,Zvi Goren
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 45,7 Mb
Release : 2002
Category : Abelian varieties
ISBN : 9780821819951
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.
