Probabilistic Diophantine Approximation
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Probabilistic Diophantine Approximation
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Author : József Beck
language : en
Publisher: Springer
Release Date : 2014-10-06
Probabilistic Diophantine Approximation written by József Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-06 with Mathematics categories.
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques. Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
Probabilistic Diophantine Approximation
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Author : Jozsef Beck
language : en
Publisher: Springer
Release Date : 2014-10-09
Probabilistic Diophantine Approximation written by Jozsef Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-09 with Mathematics categories.
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques. Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
Mixing Sequences Of Random Variables And Probabilistic Number Theory
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Author : Walter Philipp
language : en
Publisher: American Mathematical Soc.
Release Date : 1971
Mixing Sequences Of Random Variables And Probabilistic Number Theory written by Walter Philipp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Additive functions categories.
The author gives a solution to the central limit problem and proves several forms of the iterated logarithm theorem and the results are then applied to the following branches of number theory: limit theorems for continued fractions and related algorithms; limit theorems in Diophantine approximations; discrepancies of sequences uniformly distributed mod one and the distribution of additive functions. In addition to new results, the major contribution of the work is the unification of the listed branches of probabilistic number theory. In particular, this is the first time that the distribution theory of additive functions has been related to metric number theory.
Fourier Analysis And Convexity
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Author : Luca Brandolini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-27
Fourier Analysis And Convexity written by Luca Brandolini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-27 with Mathematics categories.
Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz’s proof of the isoperimetric inequality using Fourier series. This unified, self-contained book presents both a broad overview of Fourier analysis and convexity, as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way.
Probabilistic And Statistical Methods In Cryptology
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Author : Daniel Neuenschwander
language : en
Publisher: Springer
Release Date : 2004-06-08
Probabilistic And Statistical Methods In Cryptology written by Daniel Neuenschwander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-08 with Computers categories.
Cryptology nowadays is one of the most important areas of applied mathematics, building on deep results and methods from various areas of mathematics. This text is devoted to the study of stochastic aspects of cryptology. Besides classical topics from cryptology, the author presents chapters on probabilistic prime number tests, factorization with quantum computers, random-number generators, pseudo-random-number generators, information theory, and the birthday paradox and meet-in-the-middle attack. In the light of the vast literature on stochastic results relevant for cryptology, this book is intended as an invitation and introduction for students, researchers, and practitioners to probabilistic and statistical issues in cryptology.
Hyperbolic Dynamics Fluctuations And Large Deviations
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Author : D. Dolgopyat
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-01
Hyperbolic Dynamics Fluctuations And Large Deviations written by D. Dolgopyat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Mathematics categories.
This volume contains the proceedings of the semester-long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland. The broad theme of the program was the long-term behavior of dynamical systems and their statistical behavior. During the last 50 years, the statistical properties of dynamical systems of many different types have been the subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on many different areas in mathematics, physics, engineering and biology. The papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas such as statistical physics, spectral theory and some aspects of number theory and geometry.
Number Theory
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Author : Kalman Gyoery
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Number Theory written by Kalman Gyoery and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
No detailed description available for "Number Theory".
Random And Quasi Random Point Sets
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Author : Peter Hellekalek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random And Quasi Random Point Sets written by Peter Hellekalek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical ("a priori") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "random" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These "quasi-random" points are produced by deterministic algorithms and should be as "super" uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets.
Proceedings Of The Sixth Berkeley Symposium On Mathematical Statistics And Probability
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Author : Lucien Marie Le Cam
language : en
Publisher: Univ of California Press
Release Date : 1972
Proceedings Of The Sixth Berkeley Symposium On Mathematical Statistics And Probability written by Lucien Marie Le Cam and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Biometry categories.
Uniform Distribution And Quasi Monte Carlo Methods
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Author : Peter Kritzer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-06-23
Uniform Distribution And Quasi Monte Carlo Methods written by Peter Kritzer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-23 with Mathematics categories.
This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.