Twisted L Functions And Monodromy

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Twisted L Functions And Monodromy

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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10

Twisted L Functions And Monodromy 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 2009-01-10 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.

Arithmetic Of L Functions

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Author : Cristian Popescu
language : en
Publisher: American Mathematical Soc.
Release Date :

Arithmetic Of L Functions written by Cristian Popescu 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.

Number Theory Analysis And Geometry

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Author : Dorian Goldfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-21

Number Theory Analysis And Geometry written by Dorian Goldfeld 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 2011-12-21 with Mathematics categories.

Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.

Ranks Of Elliptic Curves And Random Matrix Theory

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Author : J. B. Conrey
language : en
Publisher: Cambridge University Press
Release Date : 2007-02-08

Ranks Of Elliptic Curves And Random Matrix Theory written by J. B. Conrey 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 2007-02-08 with Mathematics categories.

This comprehensive volume introduces elliptic curves and the fundamentals of modeling by a family of random matrices.

Contributions To Automorphic Forms Geometry And Number Theory

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Author : Haruzo Hida
language : en
Publisher: JHU Press
Release Date : 2004-03-11

Contributions To Automorphic Forms Geometry And Number Theory written by Haruzo Hida and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-11 with Mathematics categories.

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.

Recent Perspectives In Random Matrix Theory And Number Theory

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Author : F. Mezzadri
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-21

Recent Perspectives In Random Matrix Theory And Number Theory written by F. Mezzadri 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 2005-06-21 with Mathematics categories.

Provides a grounding in random matrix techniques applied to analytic number theory.

Analytic Number Theory

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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.

Annales Scientifiques De L Cole Normale Sup Rieure

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Author : École normale supérieure (France)
language : en
Publisher:
Release Date : 2016

Annales Scientifiques De L Cole Normale Sup Rieure written by École normale supérieure (France) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Electronic journals categories.

Current Trends In Number Theory

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Author : S.D. Adhikari
language : en
Publisher: Hindustan Book Agency and Indian National Science Academy
Release Date : 2002

Current Trends In Number Theory written by S.D. Adhikari and has been published by Hindustan Book Agency and Indian National Science Academy this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The book gives a glimpse of current research in combinatorial, algebraic, and analytic aspects of number theory. The articles are refereed and expanded versions of talks given at the International Conference on Number Theory held at the Harish-Chandra Research Institute (Allahaba, India). Included also are some articles on arithmetic algebraic geometry.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2008

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 2008 with Mathematics categories.