Title | Emerging Applications of Number Theory [electronic resource] / edited by Dennis A. Hejhal, Joel Friedman, Martin C. Gutzwiller, Andrew M. Odlyzko |
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Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1544-8 |
Descript | XIII, 697 p. online resource |
Trace formula for quantum integrable systems, lattice-point problem, and small divisors -- Theta-lifts of Maass waveforms -- The transfer operator approach to Selbergโs zeta function and modular and Maass wave forms for PSL (2, ?) -- 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 Iharaโs theorem -- Playing billiards with microwaves โ 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 -- List of Participants -- Program Schedule -- Afterword