Equidistribution In Number Theory An Introduction
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Equidistribution in Number Theory, An Introduction
Author: Andrew Granville
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-04-08
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.
Ergodic Theory
Author: Manfred Einsiedler
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-09-11
This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
An Introduction to Probabilistic Number Theory
Author: Emmanuel Kowalski
language: en
Publisher: Cambridge University Press
Release Date: 2021-05-06
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.