Arithmetical Investigations (Record no. 31187)
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000 -LEADER | |
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fixed length control field | 03207nam a22004575i 4500 |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
ISBN | 9783540783794 |
-- | 978-3-540-78379-4 |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 512.7 |
245 10 - TITLE STATEMENT | |
Title | Arithmetical Investigations |
Sub Title | Representation Theory, Orthogonal Polynomials, and Quantum Interpolations / |
Statement of responsibility, etc | edited by Shai M. J. Haran. |
260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
Place of publication | Berlin, Heidelberg : |
Name of publisher | Springer Berlin Heidelberg, |
Year of publication | 2008. |
300 ## - PHYSICAL DESCRIPTION | |
Other physical details | online resource. |
490 1# - SERIES STATEMENT | |
Series statement | Lecture Notes in Mathematics, |
505 0# - FORMATTED CONTENTS NOTE | |
Formatted contents note | Introduction: Motivations from Geometry -- Gamma and Beta Measures -- Markov Chains -- Real Beta Chain and q-Interpolation -- Ladder Structure -- q-Interpolation of Local Tate Thesis -- Pure Basis and Semi-Group -- Higher Dimensional Theory -- Real Grassmann Manifold -- p-Adic Grassmann Manifold -- q-Grassmann Manifold -- Quantum Group Uq(su(1, 1)) and the q-Hahn Basis. |
520 ## - SUMMARY, ETC. | |
Summary, etc | 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. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Mathematics. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Number theory. |
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Mathematics. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Number Theory. |
700 1# - ADDED ENTRY--PERSONAL NAME | |
Personal name | Haran, Shai M. J. |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-540-78379-4 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
Koha item type | E-BOOKS |
264 #1 - | |
-- | Berlin, Heidelberg : |
-- | Springer Berlin Heidelberg, |
-- | 2008. |
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338 ## - | |
-- | online resource |
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347 ## - | |
-- | text file |
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830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
-- | 0075-8434 ; |
Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
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IMSc Library | EBK1893 | http://dx.doi.org/10.1007/978-3-540-78379-4 | E-BOOKS |