The seven articles in this stimulating collection are surveys of a range of contemporary problems arising in physics, number theory and the interface between the two. The topics covered include arithmetic aspects of aperiodic crystals (articles by J.-L. Verger-Gaugry; and J.-P. Gazeau, Z. Masáková and E. Pelantová), phase-locking (both in classical and quantum systems) and number theory (M. Planat), Hopf algebras in renormalization theory (Ch. Bergbauer and D. Kreimer), L-functions and random matrices (E. Royer), recent applications of Kloosterman sums (P. Michel) and recent progress on the p-adic Langlands programme (A. Mézard). The book offers interesting material both for mathematicians and theoretical physicists.

Reviewer:

jnek