**AMS Chelsea Publishing**

Volume: 382;
1969;
426 pp;
Hardcover

MSC: Primary 22;
Secondary 11

**Print ISBN: 978-1-4704-2664-4
Product Code: CHEL/382.H**

List Price: $50.00

AMS Member Price: $45.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-4704-3127-3
Product Code: CHEL/382.H.E**

List Price: $50.00

AMS Member Price: $45.00

MAA Member Price: $45.00

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# Generalized Functions, Volume 6: Representation Theory and Automorphic Functions

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*I. M. Gel′fand; M. I. Graev; I. I. Pyatetskii-Shapiro*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

The first systematic theory of generalized
functions (also known as distributions) was created in the early 1950s,
although some aspects were developed much earlier, most notably in the
definition of the Green's function in mathematics and in the work of
Paul Dirac on quantum electrodynamics in physics. The six-volume
collection, Generalized Functions, written by I. M. Gel′fand
and co-authors and published in Russian between 1958 and 1966, gives an
introduction to generalized functions and presents various
applications to analysis, PDE, stochastic processes, and
representation theory.

The unifying theme of Volume 6 is the study of representations of
the general linear group of order two over various fields and rings of
number-theoretic nature, most importantly over local fields
(\(p\)-adic fields and fields of power series over finite
fields) and over the ring of adeles. Representation theory of the
latter group naturally leads to the study of automorphic functions and
related number-theoretic problems. The book contains a wealth of
information about discrete subgroups and automorphic representations,
and can be used both as a very good introduction to the subject and as
a valuable reference.

#### Readership

Graduate students and research mathematicians interested in representation theory and automorphic forms.

#### Table of Contents

# Table of Contents

## Generalized Functions, Volume 6: Representation Theory and Automorphic Functions

- Cover Cover11
- Title page iii4
- Preface v6
- Note ix10
- Contents xi12
- Chapter 1. Homogeneous spaces with a discrete stability group 118
- Chapter 2. Representations of the group of unimodular matrices of order 2 with elements from a locally compact topological field 120137
- Chapter 3. Representations of adele groups 242259
- Guide to the literature 414431
- Bibliography 417434
- Index of names 421438
- Subject index 423440
- Back Cover Back Cover1450