Some Probabilistic Theorems on Diophantine Approximations PDF Download
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Author: Harry Kesten
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 92
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Book Description
Some metrical theorems on diophantine approximations are proved. The last theorem concerns simultaneous diophantine approximations.
Author: Harry Kesten
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 92
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Book Description
Some metrical theorems on diophantine approximations are proved. The last theorem concerns simultaneous diophantine approximations.
Author: József Beck
Publisher: Springer
ISBN: 3319107410
Category : Mathematics
Languages : en
Pages : 497
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Book Description
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.
Author: Jozsef Beck
Publisher: Springer
ISBN: 9783319107424
Category : Mathematics
Languages : en
Pages : 487
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Book Description
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.
Author: Kai-Man Andy Tsang
Publisher: Open Dissertation Press
ISBN: 9781374736498
Category :
Languages : en
Pages :
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Book Description
This dissertation, "Some Theorems in Diophantine Approximation" by Kai-man, Andy, Tsang, 曾啓文, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. DOI: 10.5353/th_b3120551
Author: THOMAS PATRICK WALKER (JR)
Publisher:
ISBN:
Category :
Languages : en
Pages : 146
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Book Description
Author: Peter Eichelsbacher
Publisher: Springer Science & Business Media
ISBN: 3642360688
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory. The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Götze, a noted expert in this field.
Author: Ivan Niven
Publisher: Courier Corporation
ISBN: 0486164705
Category : Mathematics
Languages : en
Pages : 82
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Book Description
This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of complex numbers, and product of complex linear forms. 1963 edition.
Author: Walter Philipp
Publisher: American Mathematical Soc.
ISBN: 0821818147
Category : Additive functions
Languages : en
Pages : 108
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Book Description
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.
Author: Defense Documentation Center (U.S.)
Publisher:
ISBN:
Category : Military art and science
Languages : en
Pages : 1540
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Book Description
Author: Hervé Queffélec
Publisher: Springer Nature
ISBN: 9811593515
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The second edition of the book includes a new chapter on the study of composition operators on the Hardy space and their complete characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition operators, and connections between these two domains which often occur through the Kronecker approximation theorem and the Bohr lift. The book initially discusses Harmonic analysis, including a sharp form of the uncertainty principle, Ergodic theory and Diophantine approximation, basics on continued fractions expansions, and the mixing property of the Gauss map and goes on to present the general theory of Dirichlet series with classes of examples connected to continued fractions, Bohr lift, sharp forms of the Bohnenblust–Hille theorem, Hardy–Dirichlet spaces, composition operators of the Hardy–Dirichlet space, and much more. Proofs throughout the book mix Hilbertian geometry, complex and harmonic analysis, number theory, and ergodic theory, featuring the richness of analytic theory of Dirichlet series. This self-contained book benefits beginners as well as researchers.
