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03658nam a22005295i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-0-387-38032-2 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20161121231206.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2008 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387380322 |
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978-0-387-38032-2 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-0-387-38032-2 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA241-247.5 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBH |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT022000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.7 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Jorgenson, Jay. |
| Relator term |
author. |
| 245 14 - TITLE STATEMENT |
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| Title |
The Heat Kernel and Theta Inversion on SL2(C) |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Jay Jorgenson, Serge Lang. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
New York, NY : |
| Name of producer, publisher, distributor, manufacturer |
Springer New York, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2008. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
X, 319 p. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Gaussians, Spherical Inversion, and the Heat Kernel -- Spherical Inversion on SL2(C) -- The Heat Gaussian and Heat Kernel -- QED, LEG, Transpose, and Casimir -- Enter ?: The General Trace Formula -- Convergence and Divergence of the Selberg Trace -- The Cuspidal and Noncuspidal Traces -- The Heat Kernel on ?\G/K -- The Fundamental Domain -- ?-Periodization of the Heat Kernel -- Heat Kernel Convolution on (?\G/K) -- Fourier-Eisenstein Eigenfunction Expansions -- The Tube Domain for ?? -- The ?/U-Fourier Expansion of Eisenstein Series -- Adjointness Formula and the ?\G-Eigenfunction Expansion -- The Eisenstein-Cuspidal Affair -- The Eisenstein Y-Asymptotics -- The Cuspidal Trace Y-Asymptotics -- Analytic Evaluations. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of SL2(Z[i]) acting on SL2(C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Group theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Analysis (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Number theory. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Number Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Group Theory and Generalizations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Algebra. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Analysis. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Lang, Serge. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9780387380315 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-387-38032-2 |
| 912 ## - |
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ZDB-2-SMA |
