By Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff

Written by means of top specialists, this publication explores numerous instructions of present learn on the interface among dynamics and analytic quantity conception. themes contain Diophantine approximation, exponential sums, Ramsey thought, ergodic conception and homogeneous dynamics. The origins of this fabric lie within the 'Dynamics and Analytic quantity conception' Easter institution held at Durham collage in 2014. Key suggestions, state-of-the-art effects, and glossy recommendations that play a vital function in modern learn are offered in a way available to younger researchers, together with PhD scholars. This publication may also be worthwhile for confirmed mathematicians. The parts mentioned comprise ubiquitous structures 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 conception. either dynamical and 'classical' ways in the direction of quantity theoretical difficulties also are provided.

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Dynamics and Analytic Number Theory (London Mathematical Society Lecture Note Series) by Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff

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