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The remarkable effectiveness of ergodic theory in number theory

2009; Sociedade Brasileira de Matemática; Volume: 17; Issue: 1 Linguagem: Inglês

10.21711/217504322009/em171

2175-0432

Alexander Arbieto, Carlos Matheus, Carlos Gustavo Moreira,

Advanced Mathematical Theories

The first two chapters are strongly based on our book [1] "Aspectos Ergódicos da Teoria dos Números" (in Portuguese) for a mini-course of the 26th Brazilian Mathematical Colloquium, which was, in turn, based on our discussions with Jimmy Santamaria in an Ergodic-Theory seminar at IMPA around Green-Tao theorem.In particular, we would like to thank Jimmy Santamaria for his decisive participation in this seminar.Also, we would like to thank Yuri Lima and Jimmy Santamaria for a careful revision of previous versions of this work.Furthermore, this book was written during the pos-doctoral stay of Carlos Matheus at Collège de France (under the supervision of Jean-Christophe Yoccoz).In particular, he is thankful to Jean-Christophe for the several interesting mathematical (and non-mathematical) discussions, advices and friendship, and the two secretaries of the Mathematics section of College de France, Dominique Bidois and Veronique Sainz, for their invaluable support and friendship