Formes Automorphes I Questions About Slopes Of Modular Forms
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Formes Automorphes I Questions About Slopes Of Modular Forms
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Author : Centre Émile Borel
language : en
Publisher:
Release Date : 2005
Formes Automorphes I Questions About Slopes Of Modular Forms written by Centre Émile Borel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume is the first of a series of two devoted to automorphic forms from a geometric and arithmetic point of view. They also deal with certain parts of the Langlands program. The themes treated in this volume include $p$-adic modular forms, the local Langlands correspondence for $GL(n)$, the cohomology of Shimura varieties, their reduction modulo $p$, and their stratification by Newton polygons. The book is suitable for graduate students and research mathematicians interested in number theory, algebra, and algebraic geometry.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
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 2006 with Mathematics categories.
Rational Points On Modular Elliptic Curves
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Author : Henri Darmon
language : en
Publisher: American Mathematical Soc.
Release Date :
Rational Points On Modular Elliptic Curves written by Henri Darmon 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 with Mathematics categories.
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
The Eigenbook
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Author : Joël Bellaïche
language : en
Publisher: Springer Nature
Release Date : 2021-08-11
The Eigenbook written by Joël Bellaïche and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-11 with Mathematics categories.
This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.
Lectures On Modular Forms
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Author : Joseph J. Lehner
language : en
Publisher: Courier Dover Publications
Release Date : 2017-05-17
Lectures On Modular Forms written by Joseph J. Lehner and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Mathematics categories.
Concise book offers expository account of theory of modular forms and its application to number theory and analysis. Substantial notes at the end of each chapter amplify the more difficult subjects. 1969 edition.
The Geometry And Cohomology Of Some Simple Shimura Varieties Am 151
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Author : Michael Harris
language : en
Publisher: Princeton University Press
Release Date : 2001-11-04
The Geometry And Cohomology Of Some Simple Shimura Varieties Am 151 written by Michael Harris 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 2001-11-04 with Mathematics categories.
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory. The local Langlands conjecture for GLn(K), where K is a p-adic field, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary. Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.
The 1 2 3 Of Modular Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2009-09-02
The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
P Adic L Functions And P Adic Representations
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Author : Bernadette Perrin-Riou
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
P Adic L Functions And P Adic Representations written by Bernadette Perrin-Riou 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 2000 with Mathematics categories.
Traditionally, p-adic L-functions have been constructed from complex L-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of p-adic L-functions coming directly from p-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of p-adic L-functions via the arithmetic theory and a conjectural definition of the p-adic L-function via its special values. Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.
On The Stabilization Of The Trace Formula
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Author : Laurent Clozel
language : en
Publisher: International Pressof Boston Incorporated
Release Date : 2011
On The Stabilization Of The Trace Formula written by Laurent Clozel and has been published by International Pressof Boston Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Exploring The Riemann Zeta Function
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Author : Hugh Montgomery
language : en
Publisher: Springer
Release Date : 2017-09-11
Exploring The Riemann Zeta Function written by Hugh Montgomery and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.
Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.