Modular Forms And Special Cycles On Shimura Curves Am 161
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Modular Forms And Special Cycles On Shimura Curves Am 161
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Author : Stephen S. Kudla
language : en
Publisher: Princeton University Press
Release Date : 2006-04-24
Modular Forms And Special Cycles On Shimura Curves Am 161 written by Stephen S. Kudla and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-24 with Mathematics categories.
Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.
Motives And Algebraic Cycles
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Author : Rob de Jeu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Motives And Algebraic Cycles written by Rob de Jeu 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 2009 with Mathematics categories.
Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic $K$-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.
Collectanea Mathematica
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Author :
language : en
Publisher:
Release Date : 2011
Collectanea Mathematica written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Modular Forms And Special Cycles On Shimura Curves
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Author : Stephen S. Kudla
language : en
Publisher: Princeton University Press
Release Date : 2006-04-04
Modular Forms And Special Cycles On Shimura Curves written by Stephen S. Kudla and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-04 with Mathematics categories.
Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.
Advances In The Theory Of Numbers
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Author : Ayşe Alaca
language : en
Publisher: Springer
Release Date : 2015-10-28
Advances In The Theory Of Numbers written by Ayşe Alaca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-28 with Mathematics categories.
The theory of numbers continues to occupy a central place in modern mathematics because of both its long history over many centuries as well as its many diverse applications to other fields such as discrete mathematics, cryptography, and coding theory. The proof by Andrew Wiles (with Richard Taylor) of Fermat’s last theorem published in 1995 illustrates the high level of difficulty of problems encountered in number-theoretic research as well as the usefulness of the new ideas arising from its proof. The thirteenth conference of the Canadian Number Theory Association was held at Carleton University, Ottawa, Ontario, Canada from June 16 to 20, 2014. Ninety-nine talks were presented at the conference on the theme of advances in the theory of numbers. Topics of the talks reflected the diversity of current trends and activities in modern number theory. These topics included modular forms, hypergeometric functions, elliptic curves, distribution of prime numbers, diophantine equations, L-functions, Diophantine approximation, and many more. This volume contains some of the papers presented at the conference. All papers were refereed. The high quality of the articles and their contribution to current research directions make this volume a must for any mathematics library and is particularly relevant to researchers and graduate students with an interest in number theory. The editors hope that this volume will serve as both a resource and an inspiration to future generations of researchers in the theory of numbers.
The Abel Prize 2008 2012
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-21
The Abel Prize 2008 2012 written by Helge Holden 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 2014-01-21 with Mathematics categories.
Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2002
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 2002 with Mathematics categories.
Modular Forms And Special Cycles On Shimura Curves
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Author : Stephen S. Kudla
language : en
Publisher:
Release Date : 1940
Modular Forms And Special Cycles On Shimura Curves written by Stephen S. Kudla and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Arithmetical algebraic geometry categories.
Special Cycles On Shimura Curves And The Shimura Lift
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Author : Siddarth Sankaran
language : en
Publisher:
Release Date : 2012
Special Cycles On Shimura Curves And The Shimura Lift written by Siddarth Sankaran and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Geometric Modular Forms And Elliptic Curves
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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2000-09-27
Geometric Modular Forms And Elliptic Curves written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-27 with Mathematics categories.
This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.