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Dynamics and Analytic Number Theory (London Mathematical by Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff

By Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff

Written through top specialists, this publication explores a number of instructions of present learn on the interface among dynamics and analytic quantity conception. issues contain Diophantine approximation, exponential sums, Ramsey thought, ergodic concept and homogeneous dynamics. The origins of this fabric lie within the 'Dynamics and Analytic quantity conception' Easter university held at Durham college in 2014. Key techniques, state-of-the-art effects, and glossy ideas that play a vital position in modern examine are awarded in a fashion obtainable to younger researchers, together with PhD scholars. This ebook can also be worthwhile for confirmed mathematicians. The components mentioned contain ubiquitous platforms and Cantor-type units in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, a number of recurrence and Ramsey conception, counting and equidistribution difficulties in homogeneous dynamics, and functions of skinny teams in quantity concept. either dynamical and 'classical' methods in the direction of quantity theoretical difficulties also are provided.

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