Emerging Applications of Number Theory
Dennis A. Hejhal, Joel Friedman, Martin C. Gutzwiller, Andrew M. Odlyzko
Springer Science & Business Media, May 21, 1999 - Mathematics - 689 pages
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.
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adjacency matrix algebra algorithm Applications arithmetic asymptotic automorphic Berry bound Cayley graphs chaotic classical closed geodesics computations conjecture conjugacy class constant construction convergence corresponding cusp forms defined denote density det(l Dirichlet discrete domain edges eigenfunctions eigenvalues Eisenstein series elements equation ergodic Euclidean example expander graphs fluctuations Gaussian geodesic flow given half plane hand side Hecke operators Hence holomorphic horocycle hyperbolic integral invariant Laplacian Lemma level spacing distribution limit linear Maass Math Mathematics matrix measure modular multiplication norm normalized number theory path Phys Poisson polynomial prime problem proof properties Proposition prove quadratic quantization quantum chaos quaternion Ramanujan graphs random walk regular graph representation resonances Riemann zeta function Sarnak Selberg semiclassical sequence spectral spectrum statistics subgroup symmetric Terras Theorem theta trace formula transform values vector vertex vertices zeros