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Arithmetical Investigations - Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Paperback, 2008 ed.) Loot Price: R1,456
Discovery Miles 14 560
Arithmetical Investigations - Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Paperback, 2008 ed.):...

Arithmetical Investigations - Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Paperback, 2008 ed.)

Shai M. J. Haran

Series: Lecture Notes in Mathematics, 1941

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Loot Price R1,456 Discovery Miles 14 560 | Repayment Terms: R136 pm x 12*

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In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp, w). The real analogue of the p-adic integers is the interval -1,1], and a probability measure w on it gives rise to a special basis for L2( -1,1], w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of -1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.

General

Imprint: Springer-Verlag
Country of origin: Germany
Series: Lecture Notes in Mathematics, 1941
Release date: May 2008
First published: May 2008
Authors: Shai M. J. Haran
Dimensions: 235 x 155 x 12mm (L x W x T)
Format: Paperback
Pages: 222
Edition: 2008 ed.
ISBN-13: 978-3-540-78378-7
Categories: Books > Science & Mathematics > Mathematics > Number theory > General
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LSN: 3-540-78378-4
Barcode: 9783540783787

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