Twisted L Functions And Monodromy

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Twisted L-Functions and Monodromy

Author : Nicholas M. Katz
Publisher : Princeton University Press
ISBN 13 : 1400824885
Total Pages : 258 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Twisted L-Functions and Monodromy by : Nicholas M. Katz

Download or read book Twisted L-Functions and Monodromy written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2009-01-10 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Annals of Mathematics Studies

Author : Nicholas M. Katz
Publisher :
ISBN 13 : 9780691091501
Total Pages : 249 pages
Book Rating : 4.0/5 (915 download)

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Book Synopsis Annals of Mathematics Studies by : Nicholas M. Katz

Download or read book Annals of Mathematics Studies written by Nicholas M. Katz and published by . This book was released on 1940 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetic of L-functions

Author : Cristian Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821886983
Total Pages : 517 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Arithmetic of L-functions by : Cristian Popescu

Download or read book Arithmetic of L-functions written by Cristian Popescu and published by American Mathematical Soc.. This book was released on with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Number Theory, Analysis and Geometry

Author : Dorian Goldfeld
Publisher : Springer Science & Business Media
ISBN 13 : 1461412609
Total Pages : 715 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Number Theory, Analysis and Geometry by : Dorian Goldfeld

Download or read book Number Theory, Analysis and Geometry written by Dorian Goldfeld and published by Springer Science & Business Media. This book was released on 2011-12-21 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : J. B. Conrey
Publisher : Cambridge University Press
ISBN 13 : 0521699649
Total Pages : 5 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Ranks of Elliptic Curves and Random Matrix Theory by : J. B. Conrey

Download or read book Ranks of Elliptic Curves and Random Matrix Theory written by J. B. Conrey and published by Cambridge University Press. This book was released on 2007-02-08 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Haruzo Hida
Publisher : JHU Press
ISBN 13 : 9780801878602
Total Pages : 946 pages
Book Rating : 4.8/5 (786 download)

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Book Synopsis Contributions to Automorphic Forms, Geometry, and Number Theory by : Haruzo Hida

Download or read book Contributions to Automorphic Forms, Geometry, and Number Theory written by Haruzo Hida and published by JHU Press. This book was released on 2004-03-11 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : F. Mezzadri
Publisher : Cambridge University Press
ISBN 13 : 0521620589
Total Pages : 530 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Recent Perspectives in Random Matrix Theory and Number Theory by : F. Mezzadri

Download or read book Recent Perspectives in Random Matrix Theory and Number Theory written by F. Mezzadri and published by Cambridge University Press. This book was released on 2005-06-21 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a grounding in random matrix techniques applied to analytic number theory.

Moments, Monodromy, and Perversity

Author : Nicholas M. Katz
Publisher : Princeton University Press
ISBN 13 : 9780691123301
Total Pages : 492 pages
Book Rating : 4.1/5 (233 download)

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Book Synopsis Moments, Monodromy, and Perversity by : Nicholas M. Katz

Download or read book Moments, Monodromy, and Perversity written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2005-10-02 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a "generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family. Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Moments, Monodromy, and Perversity, Nicholas Katz develops new techniques, which are resolutely global in nature. They are based on two vital ingredients, neither of which existed at the time of Deligne's original work on the subject. The first is the theory of perverse sheaves, pioneered by Goresky and MacPherson in the topological setting and then brilliantly transposed to algebraic geometry by Beilinson, Bernstein, Deligne, and Gabber. The second is Larsen's Alternative, which very nearly characterizes classical groups by their fourth moments. These new techniques, which are of great interest in their own right, are first developed and then used to calculate the geometric monodromy groups attached to some quite specific universal families of (L-functions attached to) character sums over finite fields.

Current Trends in Number Theory

Author : S.D. Adhikari
Publisher : Hindustan Book Agency and Indian National Science Academy
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Current Trends in Number Theory by : S.D. Adhikari

Download or read book Current Trends in Number Theory written by S.D. Adhikari and published by Hindustan Book Agency and Indian National Science Academy. This book was released on 2002 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Functional Equation of the Twisted L-function Associated with an Automorphic Form on GL(3,R)

Author : Timothy Wayne Flood
Publisher :
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.:/5 (292 download)

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Book Synopsis The Functional Equation of the Twisted L-function Associated with an Automorphic Form on GL(3,R) by : Timothy Wayne Flood

Download or read book The Functional Equation of the Twisted L-function Associated with an Automorphic Form on GL(3,R) written by Timothy Wayne Flood and published by . This book was released on 1993 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 866 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Annals of Mathematics Studies

Author : Nicholas M. Katz
Publisher :
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.:/5 (8 download)

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Book Synopsis Annals of Mathematics Studies by : Nicholas M. Katz

Download or read book Annals of Mathematics Studies written by Nicholas M. Katz and published by . This book was released on 1940 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:

American journal of mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.:/5 (51 download)

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Book Synopsis American journal of mathematics by :

Download or read book American journal of mathematics written by and published by . This book was released on 2005 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions

Author : Valentin Blomer
Publisher : American Mathematical Society
ISBN 13 : 1470456788
Total Pages : 160 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions by : Valentin Blomer

Download or read book The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions written by Valentin Blomer and published by American Mathematical Society. This book was released on 2023-02-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

On a Mean Value of Twisted Automorphic L-Functions

Author : Chen Xu
Publisher : Open Dissertation Press
ISBN 13 : 9781361479834
Total Pages : pages
Book Rating : 4.4/5 (798 download)

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Book Synopsis On a Mean Value of Twisted Automorphic L-Functions by : Chen Xu

Download or read book On a Mean Value of Twisted Automorphic L-Functions written by Chen Xu and published by Open Dissertation Press. This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On a Mean Value of Twisted Automorphic L-functions" by Chen, Xu, 徐晨, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. DOI: 10.5353/th_b4088778 Subjects: Automorphic forms L-functions

Books in Print Supplement

Author :
Publisher :
ISBN 13 :
Total Pages : 2576 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Books in Print Supplement by :

Download or read book Books in Print Supplement written by and published by . This book was released on 2002 with total page 2576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Analytic Number Theory: L-Functions

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
ISBN 13 : 0821842668
Total Pages : 313 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advanced Analytic Number Theory: L-Functions by : Carlos J. Moreno

Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno and published by American Mathematical Soc.. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.