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Generalized functions. Volume 6, Representation theory and automorphic functions / I. M. Gel'fand, M. I. Graev, I. I. Pyatetskii-Shapiro ; translated by K. A. Hirsch.
- Format:
- Book
- Author/Creator:
- Gel'fand, I. M., author.
- Graev, M. I., author.
- Pyatetskii-Shapiro, I. I., author.
- Series:
- AMS Chelsea Publishing, v. 382
- Standardized Title:
- Obobshchennye funkt︠s︡ii. English
- Language:
- English
- Subjects (All):
- Algebraic number theory.
- Automorphic forms.
- Shimura varieties.
- Physical Description:
- 1 online resource (450 pages)
- Edition:
- [2016 edition].
- Place of Publication:
- Providence, Rhode Island : AMS Chelsea Publishing, 2016.
- Summary:
- 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.
- Notes:
- Originally published in Russian in 1958.
- Originally published in English as 5 volume set: New York : Academic Press, 1964-[1968].
- Includes bibliographical references and index.
- Description based on online resource; title from PDF title page (ebrary, viewed April 11, 2017).
- ISBN:
- 1-4704-3127-0
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