Author: Armand BorelPublisher: Cambridge University Press
ISBN: 9780521580496
Category : Mathematics
Languages : en
Pages : 226
Book Description
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.
Automorphic Forms on SL2 (R)
Author: Armand BorelPublisher: Cambridge University Press
ISBN: 9780521580496
Category : Mathematics
Languages : en
Pages : 226
Book Description
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.
Automorphic Forms
Author: Anton DeitmarPublisher: Springer Science & Business Media
ISBN: 144714435X
Category : Mathematics
Languages : en
Pages : 255
Book Description
Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Automorphic Forms, Representations and $L$-Functions
Author: Armand BorelPublisher: American Mathematical Soc.
ISBN: 0821814370
Category : Mathematics
Languages : en
Pages : 394
Book Description
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Automorphic Forms on GL (3,TR)
Author: D. BumpPublisher: Springer
ISBN: 3540390553
Category : Mathematics
Languages : en
Pages : 196
Book Description
Automorphic Forms on GL (2)
Author: H. JacquetPublisher: Springer
ISBN: 3540376127
Category : Mathematics
Languages : en
Pages : 156
Book Description
Spectral Methods of Automorphic Forms
Author: Henryk IwaniecPublisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
ISBN: 1470466228
Category : Mathematics
Languages : en
Pages : 220
Book Description
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
Automorphic Forms on SL2 (R)
Author: Armand BorelPublisher: Cambridge University Press
ISBN: 1316582639
Category : Mathematics
Languages : en
Pages : 204
Book Description
This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book.
Modern Analysis of Automorphic Forms By Example
Author: Paul GarrettPublisher: Cambridge University Press
ISBN: 1107154006
Category : Mathematics
Languages : en
Pages : 407
Book Description
Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
The 1-2-3 of Modular Forms
Author: Jan Hendrik BruinierPublisher: Springer Science & Business Media
ISBN: 3540741194
Category : Mathematics
Languages : en
Pages : 273
Book Description
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Holomorphic Automorphic Forms and Cohomology
Author: Roelof BruggemanPublisher: American Mathematical Soc.
ISBN: 1470428555
Category : Mathematics
Languages : en
Pages : 182
Book Description