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Emerging Applications of Number Theory : The IMA Volumes in Mathematics and its Applications - Dennis A. Heijhal

Emerging Applications of Number Theory

The IMA Volumes in Mathematics and its Applications

By: Dennis A. Heijhal (Editor), Joel Friedman (Editor), Martin C. Gutzwiller (Editor), Andrew M. Odlyzko (Editor)

Hardcover Published: 21st May 1999
ISBN: 9780387988245
Number Of Pages: 697

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Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Trace formula for quantum integrable systems, lattice-point problem, and small divisorsp. 1
Theta-lifts of Maass waveformsp. 39
The transfer operator approach to Selberg's zeta function and modular and Maass wave forms for PSL (2,Z)p. 73
Chaos and deviation from uniform distribution: eigenfunction computation; applied modular arithmeticp. 143
Logarithmic Sobolev techniques for random walks on graphsp. 175
Eigenvalue statistics in quantum ideal gasesp. 187
Multifractal spectrum and Laplace spectrump. 201
Number theory and atomic densitiesp. 205
Explicit formulas and oscillationsp. 219
Energy fluctuation analysis in integrable billiards in hyperbolic geometryp. 269
On eigenfunctions of the Laplacian for Hecke triangle groupsp. 291
Eigenvalue spacings for regular graphsp. 317
Classical limits of eigenfunctions for some completely integrable systemsp. 329
Does a quantum particle know the time?p. 355
Level spacings for Cayley graphsp. 373
Eigenvalues of Ramanujan graphsp. 387
Theta sums, Eisenstein series, and the semiclassical dynamics of a precessing spinp. 405
Random walks on generalized Euclidean graphsp. 451
Two proofs of Ihara's theoremp. 469
Playing billiards with microwaves - quantum manifestations of classical chaosp. 479
Characters of the symmetric groups: formulas, estimates and applicationsp. 525
Number theory and formal languagesp. 547
Expander graphs and amenable quotientsp. 571
Ramanujan hypergraphs and Ramanujan geometriesp. 583
Constructing error-correcting codes from expander graphsp. 591
Multipath zeta functions of graphsp. 601
Eigenvalues of the Laplacian for Bianchi groupsp. 617
A survey of discrete trace formulasp. 643
List of Participantsp. 683
Program Schedulep. 685
Afterwordp. 689
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387988245
ISBN-10: 0387988246
Series: The IMA Volumes in Mathematics and its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 697
Published: 21st May 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 4.45
Weight (kg): 2.57

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