Twisted L Functions And Monodromy Am 150
DOWNLOAD
Download Twisted L Functions And Monodromy Am 150 PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Twisted L Functions And Monodromy Am 150 book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Twisted L Functions And Monodromy Am 150
DOWNLOAD
Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2002-02-24
Twisted L Functions And Monodromy Am 150 written by Nicholas M. Katz 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 2002-02-24 with Mathematics categories.
For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
Analytic Number Theory
DOWNLOAD
Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-10-14
Analytic Number Theory written by Henryk Iwaniec 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 2021-10-14 with Education categories.
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Eisenstein Series And Automorphic L Functions
DOWNLOAD
Author : Freydoon Shahidi
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Eisenstein Series And Automorphic L Functions written by Freydoon Shahidi 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 2010 with Mathematics categories.
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
The Eigenbook
DOWNLOAD
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.
Simple Algebras Base Change And The Advanced Theory Of The Trace Formula
DOWNLOAD
Author : James Arthur
language : en
Publisher: Princeton University Press
Release Date : 1989-06-21
Simple Algebras Base Change And The Advanced Theory Of The Trace Formula written by James Arthur 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 1989-06-21 with Mathematics categories.
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
The Geometry Of Schemes
DOWNLOAD
Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
The Geometry Of Schemes written by David Eisenbud 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 2006-04-06 with Mathematics categories.
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Period Mappings And Period Domains
DOWNLOAD
Author : James A. Carlson
language : en
Publisher:
Release Date : 2017
Period Mappings And Period Domains written by James A. Carlson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Geometry, Algebraic categories.
This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether–Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford–Tate groups and their associated domains, the Mumford–Tate varieties and generalizations of Shimura varieties.
Lectures On K3 Surfaces
DOWNLOAD
Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26
Lectures On K3 Surfaces written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.
Hodge Theory
DOWNLOAD
Author : Eduardo Cattani
language : en
Publisher: Princeton University Press
Release Date : 2014-07-21
Hodge Theory written by Eduardo Cattani 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 2014-07-21 with Mathematics categories.
This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
An Introduction To Probabilistic Number Theory
DOWNLOAD
Author : Emmanuel Kowalski
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-06
An Introduction To Probabilistic Number Theory written by Emmanuel Kowalski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.