Automorphic Forms And Galois Representations

Author : Fred Diamond
Publisher :
ISBN 13 : 9781316071786
Total Pages : 374 pages
Book Rating : 4.82/5 ( download)

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Download or read book Automorphic Forms and Galois Representations written by Fred Diamond and published by . This book was released on 2014 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.

Author : Jean-Pierre Serre
Publisher : CRC Press
ISBN 13 : 1439863865
Total Pages : 203 pages
Book Rating : 4.62/5 ( download)

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Download or read book Abelian l-Adic Representations and Elliptic Curves written by Jean-Pierre Serre and published by CRC Press. This book was released on 1997-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one

Author : Bas Edixhoven
Publisher : Princeton University Press
ISBN 13 : 1400839009
Total Pages : 438 pages
Book Rating : 4.01/5 ( download)

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Download or read book Computational Aspects of Modular Forms and Galois Representations written by Bas Edixhoven and published by Princeton University Press. This book was released on 2011-05-31 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.

Author : Toshiyuki Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 0817646469
Total Pages : 220 pages
Book Rating : 4.62/5 ( download)

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Download or read book Representation Theory and Automorphic Forms written by Toshiyuki Kobayashi and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

Author : D. Bump
Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.58/5 ( download)

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Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Fred Diamond
Publisher : Cambridge University Press
ISBN 13 : 1107691923
Total Pages : 385 pages
Book Rating : 4.26/5 ( download)

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Download or read book Automorphic Forms and Galois Representations written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Author : Fred Diamond
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.41/5 ( download)

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Download or read book Automorphic Forms and Galois Representations written by Fred Diamond and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Haruzo Hida
Publisher : Cambridge University Press
ISBN 13 : 9780521770361
Total Pages : 358 pages
Book Rating : 4.6X/5 ( download)

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Download or read book Modular Forms and Galois Cohomology written by Haruzo Hida and published by Cambridge University Press. This book was released on 2000-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.

Author : Fred Diamond
Publisher : Springer Science & Business Media
ISBN 13 : 0387272267
Total Pages : 450 pages
Book Rating : 4.69/5 ( download)

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Download or read book A First Course in Modular Forms written by Fred Diamond and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

Author : H. Jacquet
Publisher : Springer
ISBN 13 : 3540376127
Total Pages : 156 pages
Book Rating : 4.25/5 ( download)

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Download or read book Automorphic Forms on GL (2) written by H. Jacquet and published by Springer. This book was released on 2006-11-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: