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| Author | : Julia Mueller |
| Publisher | : Cambridge University Press |
| Total Pages | : 451 |
| Release | : 2021-08-05 |
| Genre | : Mathematics |
| ISBN | : 1108710948 |
A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.
| Author | : Julia Mueller |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 2021-08-05 |
| Genre | : Mathematics |
| ISBN | : 1108619959 |
Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.
| Author | : A. J. Scholl |
| Publisher | : Cambridge University Press |
| Total Pages | : 506 |
| Release | : 1998-11-26 |
| Genre | : Mathematics |
| ISBN | : 0521644194 |
Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
| Author | : Bruno Kahn |
| Publisher | : Cambridge University Press |
| Total Pages | : 217 |
| Release | : 2020-05-07 |
| Genre | : Mathematics |
| ISBN | : 1108574912 |
The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
| Author | : Steven George Krantz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 328 |
| Release | : 2009 |
| Genre | : Education |
| ISBN | : 0821846299 |
"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.
| Author | : S. J. Patterson |
| Publisher | : Cambridge University Press |
| Total Pages | : 176 |
| Release | : 1995-02-02 |
| Genre | : Mathematics |
| ISBN | : 9780521499057 |
An introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function. It emphasizes central ideas of broad application, avoiding technical results and the customary function-theoretic appro
| Author | : Joseph Bernstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 283 |
| Release | : 2013-12-11 |
| Genre | : 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 | : Eng-chye Tan |
| Publisher | : World Scientific |
| Total Pages | : 426 |
| Release | : 2004 |
| Genre | : Science |
| ISBN | : 981238779X |
The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on ?Representation Theory of Lie Groups? from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadi? from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pand?i? from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.
| Author | : Roger Godement |
| Publisher | : Springer |
| Total Pages | : 200 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540374361 |
| Author | : Lin Weng |
| Publisher | : World Scientific |
| Total Pages | : 411 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 981256814X |
Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.
