Author: Florin SpinuPublisher:
ISBN:
Category : Eisenstein series
Languages : en
Pages : 66
Book Description
The Eisenstein Series of SL(2, R)
Author: Florin SpinuPublisher:
ISBN:
Category : Eisenstein series
Languages : en
Pages : 66
Book Description
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.
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.
Posn(R) and Eisenstein Series
Author: Publisher: Springer Science & Business Media
ISBN: 9783540257875
Category : Eisenstein series
Languages : en
Pages : 186
Book Description
SL2(R)
Author: S. LangPublisher: Springer Science & Business Media
ISBN: 1461251427
Category : Mathematics
Languages : en
Pages : 432
Book Description
SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.
SL2(R)
Author: S. LangPublisher: Springer Science & Business Media
ISBN: 9780387961989
Category : Mathematics
Languages : en
Pages : 456
Book Description
This book introduces the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). The contents are accessible to a wide audience, requiring only a knowledge of real analysis, and some differential equations.
Automorphic Forms on GL (3,TR)
Author: D. BumpPublisher: Springer
ISBN: 3540390553
Category : Mathematics
Languages : en
Pages : 196
Book Description
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.
Eisenstein Series and Applications
Author: Wee Teck GanPublisher: Springer Science & Business Media
ISBN: 0817646396
Category : Mathematics
Languages : en
Pages : 317
Book Description
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.
Analysis IV
Author: Roger GodementPublisher: Springer
ISBN: 3319169076
Category : Mathematics
Languages : en
Pages : 535
Book Description
Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.