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Emerging Applications of Number Theory /

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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 a...

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Bibliographic Details
Main Author: Hejhal, Dennis A.
Corporate Author: SpringerLink (Online service)
Other Authors: Friedman, Joel, Gutzwiller, M. C. (Martin C.), Odlyzko, A. M.
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1999.
Series:IMA volumes in mathematics and its applications ; 109.
Subjects:
Mathematics.
Combinatorial analysis.
Number theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Trace formula for quantum integrable systems, lattice-point problem, and small divisors
  • Theta-lifts of Maass waveforms
  • The transfer operator approach to Selberg's zeta function and modular and Maass wave forms for PSL (2,ZZ)
  • Chaos and deviation from uniform distribution: eigenfunction computation; applied modular arithmetic
  • Logarithmic Sobolev techniques for random walks on graphs
  • Eigenvalue statistics in quantum ideal gases
  • Multifractal spectrum and Laplace spectrum
  • Number theory and atomic densities
  • Explicit formulas and oscillations
  • Energy fluctuation analysis in integrable billiards;- in hyperbolic geometry
  • On eigenfunctions of the Laplacian for Hecke triangle groups
  • Eigenvalue spacings for regular graphs
  • Classical limits of eigenfunctions for some completely integrable systems
  • Does a quantum particle know the time?- Level spacings for Cayley graphs
  • Eigenvalues of Ramanujan graphs
  • Theta sums, Eisenstein series, and the semiclassical dynamics of a precessing spin
  • Random walks on generalized Euclidean graphs
  • Two proofs of Ihara's theorem
  • Playing billiards with microwaves
  • Quantum manifestations of classical chaos
  • Characters of the symmetric groups: formulas, estimates and applications
  • Number theory and formal languages
  • Expander graphs and amenable quotients
  • Ramanujan hypergraphs and Ramanujan geometries
  • Constructing error-correcting codes from expander graphs
  • Multipath zeta functions of graphs
  • Eigenvalues of the Laplacian for Bianchi groups
  • A survey of discrete trace formulas.