دانلود کتاب The remarkable effectiveness of ergodic theory in number theory

Abstract. The main goal of this survey is the description of the fruitfulinteraction between Ergodic Theory and Number Theory via the study oftwo beautiful results: the first one by Ben Green and Terence Tao (aboutlong arithmetic progressions of primes) and the second one by Noam Elkiesand CurtisMcMullen (about the distribution of the sequence {ãn} mod 1).More precisely, during the first part, we will see how the ergodic-theoreticalideas of Furstenberg about the famous SzemerLedi theorem were greatlygeneralized by Green and Tao in order to solve the classical problem offinding arbitrarily long arithmetical progression of prime numbers, whilethe second part will focus on how Elkies and McMullen used the ideasof Ratnerfs theory (about the classification of ergodic measures related tounipotent dynamics) to compute explicitly the distribution of the sequence{ãn} on the unit circle.