Periods of Hilbert Modular Surfaces
Author: T. Oda
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 141
ISBN-13: 1468492012
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Periods of Hilbert Modular Surfaces
Author: T. Oda
Publisher:
Published: 1982-01-01
Total Pages: 144
ISBN-13: 9781468492026
DOWNLOAD EBOOK →Hilbert Modular Surfaces
Author: Gerard van der Geer
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 301
ISBN-13: 3642615538
DOWNLOAD EBOOK →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 Surfaces
Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change
Author: Jayce Getz
Publisher: Springer Science & Business Media
Published: 2012-03-28
Total Pages: 264
ISBN-13: 3034803516
DOWNLOAD EBOOK →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.
Algebraic Cycles and Motives: Volume 1
Author: Jan Nagel
Publisher: Cambridge University Press
Published: 2007-05-03
Total Pages: 293
ISBN-13: 0521701740
DOWNLOAD EBOOK →This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Intersections of Hirzebruch–Zagier Divisors and CM Cycles
Author: Benjamin Howard
Publisher: Springer
Published: 2012-01-05
Total Pages: 146
ISBN-13: 364223979X
DOWNLOAD EBOOK →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.
Contributions to Automorphic Forms, Geometry, and Number Theory
Author: Haruzo Hida
Publisher: JHU Press
Published: 2004-03-11
Total Pages: 946
ISBN-13: 9780801878602
DOWNLOAD EBOOK →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.
Intersections of Hirzebruch–Zagier Divisors and CM Cycles
Author: Benjamin Howard
Publisher: Springer Science & Business Media
Published: 2012-01-06
Total Pages: 146
ISBN-13: 3642239781
DOWNLOAD EBOOK →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.
Cohomology of Arithmetic Groups and Automorphic Forms
Author: Jean-Pierre Labesse
Publisher: Springer
Published: 2006-11-14
Total Pages: 358
ISBN-13: 3540468765
DOWNLOAD EBOOK →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.
