Distribution Modulo One And Diophantine Approximation
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Distribution Modulo One and Diophantine Approximation
Author: Yann Bugeaud
language: en
Publisher: Cambridge University Press
Release Date: 2012-07-05
A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.
Applications of Diophantine Approximation to Integral Points and Transcendence
Author: Pietro Corvaja
language: en
Publisher: Cambridge University Press
Release Date: 2018-05-03
Introduction to Diophantine approximation and equations focusing on Schmidt's subspace theorem, with applications to transcendence.
Sequences, Discrepancies and Applications
The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.