... Duke-Friedlander-Iwaniec, Kowalski-Michel-Vanderkam, Ju-tila, Motohashi, Ivic, Soundararajan, Rubinstein, and others on moments offamilies of L-functions which provide the evidence for the random ... by the random matrix statistics typical for chaotic models.The origin of this peculiarity can be traced to the existence in arithmeticsystems of a very large number of periodic orbits with exactly ... Spectral Statistics and Periodic Orbits, in Proceedings of theInternational School of Physics ‘Enrico Fermi’, Varenna (1999), New DirectionsQuantum and Arithmetical Chaos 105in Quantum Chaos,...