Arithmetical Investigations (Record no. 10136)
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fixed length control field | 03273nam a22004455i 4500 |
001 - CONTROL NUMBER | |
control field | 978-3-540-78379-4 |
003 - CONTROL NUMBER IDENTIFIER | |
control field | DE-He213 |
005 - DATE AND TIME OF LATEST TRANSACTION | |
control field | 20190213151259.0 |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
fixed length control field | cr nn 008mamaa |
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fixed length control field | 100301s2008 gw | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9783540783794 |
-- | 978-3-540-78379-4 |
024 7# - OTHER STANDARD IDENTIFIER | |
Standard number or code | 10.1007/978-3-540-78379-4 |
Source of number or code | doi |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
Classification number | QA241-247.5 |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBH |
Source | bicssc |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | MAT022000 |
Source | bisacsh |
072 #7 - SUBJECT CATEGORY CODE | |
Subject category code | PBH |
Source | thema |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 512.7 |
Edition number | 23 |
245 10 - TITLE STATEMENT | |
Title | Arithmetical Investigations |
Medium | [electronic resource] : |
Remainder of title | Representation Theory, Orthogonal Polynomials, and Quantum Interpolations / |
Statement of responsibility, etc | edited by Shai M. J. Haran. |
264 #1 - | |
-- | Berlin, Heidelberg : |
-- | Springer Berlin Heidelberg, |
-- | 2008. |
300 ## - PHYSICAL DESCRIPTION | |
Extent | XII, 222 p. 23 illus. |
Other physical details | online resource. |
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-- | online resource |
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-- | text file |
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490 1# - SERIES STATEMENT | |
Series statement | Lecture Notes in Mathematics, |
International Standard Serial Number | 0075-8434 |
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 or geographic name as entry element | Number theory. |
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical term or geographic name as entry element | Number Theory. |
-- | http://scigraph.springernature.com/things/product-market-codes/M25001 |
700 1# - ADDED ENTRY--PERSONAL NAME | |
Personal name | Haran, Shai M. J. |
Relator term | editor. |
Relator code | edt |
-- | http://id.loc.gov/vocabulary/relators/edt |
710 2# - ADDED ENTRY--CORPORATE NAME | |
Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY | |
Title | Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783540849216 |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
Display text | Printed edition: |
International Standard Book Number | 9783540783787 |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
Uniform title | Lecture Notes in Mathematics, |
-- | 0075-8434 |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | https://doi.org/10.1007/978-3-540-78379-4 |
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