Intersection Homology Of Hilbert Modular Varieties And Quadratic Base Change
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Hilbert Modular Forms With Coefficients In Intersection Homology And Quadratic Base Change
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Author : Jayce Getz
language : en
Publisher: Birkhäuser
Release Date : 2012-04-05
Hilbert Modular Forms With Coefficients In Intersection Homology And Quadratic Base Change written by Jayce Getz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-05 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 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.
Intersection Homology Of Hilbert Modular Varieties And Quadratic Base Change
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Author : Jayce Getz
language : en
Publisher:
Release Date : 2007
Intersection Homology Of Hilbert Modular Varieties And Quadratic Base Change written by Jayce Getz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Intersections Of Hirzebruch Zagier Divisors And Cm Cycles
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Author : Benjamin Howard
language : en
Publisher: Springer
Release Date : 2012-01-05
Intersections Of Hirzebruch Zagier Divisors And Cm Cycles written by Benjamin Howard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Mathematics categories.
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.
An Introduction To Automorphic Representations
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Author : Jayce R. Getz
language : en
Publisher: Springer Nature
Release Date : 2024-03-01
An Introduction To Automorphic Representations written by Jayce R. Getz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-01 with Mathematics categories.
The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics. The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed. This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface.
Lie Models In Topology
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Author : Urtzi Buijs
language : en
Publisher: Springer Nature
Release Date : 2020-12-15
Lie Models In Topology written by Urtzi Buijs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.
Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version. In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Reviews In Number Theory 1973 83
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Author : Richard K. Guy
language : en
Publisher:
Release Date : 1984
Reviews In Number Theory 1973 83 written by Richard K. Guy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematical reviews categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Comprehensive Dissertation Index
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Author :
language : en
Publisher:
Release Date : 1989
Comprehensive Dissertation Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Dissertations, Academic categories.
Modular Forms A Computational Approach
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Author : William A. Stein
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-02-13
Modular Forms A Computational Approach written by William A. Stein 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 2007-02-13 with Mathematics categories.
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.