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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.

- Series:
**259** - Author:
**Manfred Einsiedler, Thomas Ward (auth.)** - Year:
**2011** - Publisher:
**Springer-Verlag London** - Language:
**English** - ISBN:
**0857290207,9780857290205**

- File size:
**3 365 745** - Format:
**pdf**

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This book is an introduction to the ergodic theory behind common number expansions, for instance decimal expansions, continued fractions and many others. The questions studied are dynamical as well as number theoretic in nature, and the answers are obtain...

Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, ...

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra an...

This text provides an introduction to ergodic theory suitable for readers knowing basic measure theory. The mathematical prerequisites are summarized in Chapter 0. It is hoped the reader will be ready to tackle research papers after reading the book. The ...

This is an introductory textbook on probability theory and its applications. Basic concepts such as probability measure, random variable, distribution, and expectation are fully treated without technical complications. Both the discrete and continuous cas...

Queueing Theory with Applications to Packet Telecommunication is an efficient introduction to fundamental concepts and principles underlying the behavior of queueing systems and its application to the design of packet-oriented electrical communication sys...

Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other ...

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progress...

This book is an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. It does not assume knowledge of measure theory; all the results needed from measure theory are presented from sc...

The aim of this series is to inform both professional philosophers and a larger readership (of social and natural scientists, methodologists, mathematicians, students, teachers, publishers, etc. ) about what is going on, who's who, and who does what in co...

The sixteenth annual symposium of the Society for the Study of Inborn Errors of Metabolism was held in Bristol from 12th to 14th July, 1978. About 25 invited speakers and 150 participants came from many parts of Europe and North America to consider the to...

For some years I have felt there was a need for a single, comprehenÂ sive, reference book on exploration geology. Numerous textbooks are available on subjects such as geophysical prospecting, exploration geochemistry, mining geology, photogeology and gene...

In September 1977 a "Regional Science Symposium" was held at the Faculty of Economics of the University of Goningen in the Netherlands. The impetus in organizing this symposium was the recent estabÂ lishmen t at the F acuIty of Economics of a group engage...

While general systems research has had a considerable impact on research in the social sciences, this impact has been mainly conceptual and has not served to provide the operational and methodological aids for research which are possible. In addition, man...

Project Set Strategies focuses on an issue of vital concern to corporate managers: the development and implementation of strategy. Regretfully, this topic has received too little attention in the literature of finance and has been treated inÂ completely i...

The productive work of widely distributed academic research has contributed substantially, over the postwar period, to important advances in our understanding. It has also offered a clearer recognition of many unresolved problems. NeverÂ theless, the prog...

''The problem of Transcendence is the problem of our time. " I Needless to say, Transcendence was a particularly lively i~sue when Karl Heim wrote these words in the mid-1930's. Within the province of philosophiÂ cal theology and philosophy of religion, h...

It is my hope that this publication of a "lost" work by Galiani will interest scholars of many nations and disciplines. Few writers could make a more compelling claim upon such a cosmopolitan audience. An Italian with deep roots in his homeland, Galiani a...

This liber amicorum honours Professor Jan Tissot van Patot as a scholar, referring in particular to his concern with transport economics. The signiÂ ficance of his work grew out of his influence within Netherlands Railways as, with the passage of the year...