Titlebook: Emerging Applications of Number Theory; Dennis A. Hejhal,Joel Friedman,Andrew M. Odlyzko Book 1999 Springer-Verlag New York, Inc. 1999 Hyp

custody

游行

Level Spacings for Cayley Graphs,mong the Cayley graphs of ..(F.) that we consider are the new expander graphs recently discovered by Y. Shalom. In addition, we use a Markov chain method to generate random 4-regular graphs, and observe that the average eigenvalue spacings are closely approximated by the Wigner surmise.

難解

defray

Multi-Threshold CMOS Digital Circuitsthods of spectral analysis, needed for high accuracy of eigenvalues and eigenstates calculations. In the second part of the talk we look at a completely different number-theoretic task—a construction of very regular, but still random, finite structures for new generation of computer chips and verification of chip designs.

苦笑

https://doi.org/10.1007/978-1-4757-3115-6cal system is shown to be related to sums of integers to the power α/(α. 1). In particular, for α = 3/2, the periodic orbits are related to sums of cubes, for which one again expects number theoretic degeneracies, with consequences for the two point correlation function.

做事過頭

記成螞蟻

Theta-Lifts of Maass Waveforms,complex upper half-plane, then ..:= ... is a compact Riemann surface. Furthermore, let Г.(.) ...(?) be the Hecke congruence group of level .. Then ..:= Г.(.). is a non-compact Riemann surface with finite volume. Let △ be the hyperbolic Laplace-operator on .. In certain situations, it is known that i

啪心兒跳動

,The Transfer Operator Approach to Selberg’s Zeta Function and Modular and Maass Wave Forms For , (2eterminant .(1 - ..) of the transfer operator .., . ∈ . for the geodesic flow on the modular surface, the zeros and poles of the Selberg function are closely related to those .values, where .. has an eigenvalue λ = 1 respectively where .. has poles. It turns out that the corresponding eigenfunctions