Author : Joseph Bernstein
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 49,62 MB
Release : 2013-12-11
Category : Mathematics
ISBN : 0817682260
This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Author : Julia Mueller
Publisher : Cambridge University Press
Page : 451 pages
File Size : 47,21 MB
Release : 2021-08-05
Category : Mathematics
ISBN : 1108710948
A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.
Author : Edward Frenkel
Publisher : Cambridge University Press
Page : 5 pages
File Size : 42,26 MB
Release : 2007-06-28
Category : Mathematics
ISBN : 0521854431
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Author : Lizhen Ji
Publisher : International Press of Boston
Page : 0 pages
File Size : 16,34 MB
Release : 2010
Category : Algebraic number theory
ISBN : 9781571461414
Consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program.
Author : Edward Frenkel
Publisher : Basic Books
Page : 314 pages
File Size : 20,78 MB
Release : 2013-10-01
Category : Mathematics
ISBN : 0465069959
An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
Author : Fred Diamond
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 16,51 MB
Release : 2006-03-30
Category : Mathematics
ISBN : 0387272267
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 : James Arthur
Publisher : Princeton University Press
Page : 252 pages
File Size : 13,45 MB
Release : 1989-06-21
Category : Mathematics
ISBN : 9780691085180
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.
Author : D. Bump
Publisher : Springer
Page : 196 pages
File Size : 37,7 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540390553
Author : Philipp Fleig
Publisher : Cambridge Studies in Advanced
Page : 587 pages
File Size : 23,10 MB
Release : 2018-07-05
Category : Mathematics
ISBN : 1107189926
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author : Gaëtan Chenevier
Publisher : Springer
Page : 428 pages
File Size : 46,58 MB
Release : 2019-02-28
Category : Mathematics
ISBN : 3319958917
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.
