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From July 11th to July 22nd, 2005, a NATO advanced study institute, as part of the series “Seminaire ´ de mathematiques ´ superieures”, ´ was held at the U- versite ´ de Montreal, ´ on the subject Equidistribution in the theory of numbers. There were about one hundred participants from sixteen countries around the world. This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have noticed incre- ing interest being paid to distribution problems, whether of rational points, of zeros of zeta functions, of eigenvalues, etc. Although these problems have been motivated from very di?erent perspectives, one nds that there is much in common, and presumably it is healthy to try to view such questions as part of a bigger subject. It is for this reason we decided to hold a school on “Equidistribution in number theory” to introduce junior researchers to these beautiful questions, and to determine whether di?erent approaches can in uence one another. There are far more good problems than we had time for in our schedule. We thus decided to focus on topics that are clearly inter-related or do not requirealotofbackgroundtounderstand.

Geometry --- Harmonic analysis. Fourier analysis --- informatietheorie --- Mathematical physics --- Number theory --- Ergodic theory. Information theory --- differentiaalvergelijkingen --- landmeetkunde --- Fourieranalyse --- getallenleer --- Irregularities of distribution (Number theory) --- Irrégularités de distribution (Théorie des nombres) --- Congresses --- Congrès --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Congresses. --- Number theory. --- Geometry, algebraic. --- Differentiable dynamical systems. --- Mathematics. --- Fourier analysis. --- Number Theory. --- Algebraic Geometry. --- Dynamical Systems and Ergodic Theory. --- Measure and Integration. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Math --- Science --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Algebraic geometry --- Number study --- Numbers, Theory of --- Algebra --- Algebraic geometry. --- Dynamics. --- Ergodic theory. --- Measure theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Ergodic transformations --- Continuous groups --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Equidistribution