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Emerging Applications of Number Theory

  • Book
  • © 1999

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Editors:
  1. Dennis A. Hejhal

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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  2. Joel Friedman

    1. Department of Mathematics, University of British Columbia, Vancouver, Canada

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  3. Martin C. Gutzwiller

    1. IBM Thomas J. Watson Research Center, Yorktown Heights, USA

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  4. Andrew M. Odlyzko

    1. AT&T Labs—Research, Florham Park, USA

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 109)

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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Trace Formula for Quantum Integrable Systems, Lattice-Point Problem, and Small Divisors

    • Pavel Bleher
    Pages 1-38

  3. Theta-Lifts of Maass Waveforms

    • Jens Bolte, Stefan Johansson
    Pages 39-72

  4. The Transfer Operator Approach to Selberg’s Zeta Function and Modular and Maass Wave Forms For P S L (2, ℤ)

    • Cheng-Hung Chang, Dieter H. Mayer
    Pages 73-141

  5. Chaos and Deviation from Uniform Distribution: Eigenfunction Computation; Applied Modular Arithmetic

    • David V. Chudnovsky, Gregory V. Chudnovsky
    Pages 143-174

  6. Logarithmic Sobolev Techniques for Random Walks on Graphs

    • Fan Chung
    Pages 175-186

  7. Eigenvalue Statistics in Quantum Ideal Gases

    • Bruno Eckhardt
    Pages 187-199

  8. Multifractal Spectrum and Laplace Spectrum

    • Isaac Efrat
    Pages 201-204

  9. Number Theory and Atomic Densities

    • Charles L. Fefferman, Luis A. Seco
    Pages 205-218

  10. Explicit Formulas and Oscillations

    • Akio Fujii
    Pages 219-267

  11. Energy Fluctuation Analysis in Integrable Billiards in Hyperbolic Geometry

    • Christian Grosche
    Pages 269-289

  12. On Eigenfunctions of the Laplacian for Hecke Triangle Groups

    • Dennis A. Hejhal
    Pages 291-315

  13. Eigenvalue Spacings for Regular Graphs

    • Dmitry Jakobson, Stephen D. Miller, Igor Rivin, ZeĂ©v Rudnick
    Pages 317-327

  14. Classical Limits of Eigenfunctions for Some Completely Integrable Systems

    • Dmitry Jakobson, Steve Zelditch
    Pages 329-354

  15. Does a Quantum Particle Know the Time?

    • Lev Kapitanski, Igor Rodnianski
    Pages 355-371

  16. Level Spacings for Cayley Graphs

    • John D. Lafferty, Daniel N. Rockmore
    Pages 373-386

  17. Eigenvalues of Ramanujan Graphs

    • Wen-Ching Winnie Li
    Pages 387-403

  18. Theta Sums, Eisenstein Series, and the Semiclassical Dynamics of a Precessing Spin

    • Jens Marklof
    Pages 405-450

  19. Random Walks on Generalized Euclidean Graphs

    • Perla Myers
    Pages 451-468

  20. Two Proofs of Ihara’s Theorem

    • Sam Northshield
    Pages 469-478
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Keywords

About this book

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.

Editors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    Dennis A. Hejhal

  • Department of Mathematics, University of British Columbia, Vancouver, Canada

    Joel Friedman

  • IBM Thomas J. Watson Research Center, Yorktown Heights, USA

    Martin C. Gutzwiller

  • AT&T Labs—Research, Florham Park, USA

    Andrew M. Odlyzko

Bibliographic Information

  • Book Title: Emerging Applications of Number Theory

  • Editors: Dennis A. Hejhal, Joel Friedman, Martin C. Gutzwiller, Andrew M. Odlyzko

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4612-1544-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1999

  • Hardcover ISBN: 978-0-387-98824-5Published: 21 May 1999

  • Softcover ISBN: 978-1-4612-7186-4Published: 21 October 2012

  • eBook ISBN: 978-1-4612-1544-8Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XIII, 697

  • Topics: Number Theory, Combinatorics

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