Automorphic Forms And Galois Representations Volume 1 PDF Download
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Author | : Fred Diamond |
Publisher | : Cambridge University Press |
Total Pages | : 385 |
Release | : 2014-10-16 |
Genre | : Mathematics |
ISBN | : 1316062333 |
Download Automorphic Forms and Galois Representations: Volume 1 Book in PDF, ePub and Kindle
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 | : Bas Edixhoven |
Publisher | : Princeton University Press |
Total Pages | : 438 |
Release | : 2011-05-31 |
Genre | : Mathematics |
ISBN | : 1400839009 |
Download Computational Aspects of Modular Forms and Galois Representations Book in PDF, ePub and Kindle
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 |
Total Pages | : 220 |
Release | : 2007-10-10 |
Genre | : Mathematics |
ISBN | : 0817646469 |
Download Representation Theory and Automorphic Forms Book in PDF, ePub and Kindle
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 | : Jean-Pierre Serre |
Publisher | : CRC Press |
Total Pages | : 203 |
Release | : 1997-11-15 |
Genre | : Mathematics |
ISBN | : 1439863865 |
Download Abelian l-Adic Representations and Elliptic Curves Book in PDF, ePub and Kindle
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 | : Joël Bellaïche |
Publisher | : Springer Nature |
Total Pages | : 319 |
Release | : 2021-08-11 |
Genre | : Mathematics |
ISBN | : 3030772632 |
Download The Eigenbook Book in PDF, ePub and Kindle
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.
Author | : Fred Diamond |
Publisher | : Cambridge University Press |
Total Pages | : 387 |
Release | : 2014-10-16 |
Genre | : Mathematics |
ISBN | : 1316062341 |
Download Automorphic Forms and Galois Representations: Volume 2 Book in PDF, ePub and Kindle
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 two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.
Author | : Fred Diamond |
Publisher | : Cambridge University Press |
Total Pages | : 387 |
Release | : 2014-10-16 |
Genre | : Mathematics |
ISBN | : 1107693632 |
Download Automorphic Forms and Galois Representations Book in PDF, ePub and Kindle
Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
Author | : Haruzo Hida |
Publisher | : Cambridge University Press |
Total Pages | : 358 |
Release | : 2000-06-29 |
Genre | : Mathematics |
ISBN | : 9780521770361 |
Download Modular Forms and Galois Cohomology Book in PDF, ePub and Kindle
Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.
Author | : H. Jacquet |
Publisher | : Springer |
Total Pages | : 156 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540376127 |
Download Automorphic Forms on GL (2) Book in PDF, ePub and Kindle
Author | : Gaëtan Chenevier |
Publisher | : Springer |
Total Pages | : 417 |
Release | : 2019-02-28 |
Genre | : Mathematics |
ISBN | : 3319958917 |
Download Automorphic Forms and Even Unimodular Lattices Book in PDF, ePub and Kindle
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.