Probabilistic Methods In The Theory Of Arithmetic Functions

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Probabilistic Methods In The Theory Of Arithmetic Functions

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Author : Gutti Joseph Babu
language : en
Publisher:
Release Date : 1973

Probabilistic Methods In The Theory Of Arithmetic Functions written by Gutti Joseph Babu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.

Probabilistic Methods In The Theory Of Arithmetic Functions

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Author : Gutti Jogesh Babu
language : en
Publisher:
Release Date : 1978

Probabilistic Methods In The Theory Of Arithmetic Functions written by Gutti Jogesh Babu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Arithmetic functions categories.

Analytic And Probabilistic Methods In Number Theory

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Author : F. Schweiger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18

Analytic And Probabilistic Methods In Number Theory written by F. Schweiger 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 2020-05-18 with Mathematics categories.

No detailed description available for "Analytic and Probabilistic Methods in Number Theory".

Probabilistic Methods In The Theory Of Numbers

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Author : Jonas Kubilius
language : en
Publisher: American Mathematical Soc.
Release Date : 1964-12-31

Probabilistic Methods In The Theory Of Numbers written by Jonas Kubilius 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 1964-12-31 with Mathematics categories.

Presents twenty-three lessons, including problems and exercises, on the use of BASIC computer language on microcomputers such as Apple, Pet, Atari, and TRS-80.

Probabilistic Number Theory Ii

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Author : P.D.T.A. Elliott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Probabilistic Number Theory Ii written by P.D.T.A. Elliott 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.

In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. The methods involve a synthesis of Probability and Number Theory; sums of independent infinitesimal random variables playing an important role. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;; z {3 (x) ) converge weakly; (see Notation). In contrast to volume one we allow {3(x) to become unbounded with x. In particular, we investigate to what extent one can simulate the behaviour of additive arithmetic functions by that of sums of suit ably defined independent random variables. This fruiful point of view was intro duced in a 1939 paper of Erdos and Kac. We obtain their (now classical) result in Chapter 12. Subsequent methods involve both Fourier analysis on the line, and the appli cation of Dirichlet series. Many additional topics are considered. We mention only: a problem of Hardy and Ramanujan; local properties of additive arithmetic functions; the rate of convergence of certain arithmetic frequencies to the normal law; the arithmetic simulation of all stable laws. As in Volume I the historical background of various results is discussed, forming an integral part of the text. In Chapters 12 and 19 these considerations are quite extensive, and an author often speaks for himself.

Introduction To Analytic And Probabilistic Number Theory

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Author : Gérald Tenenbaum
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-07-16

Introduction To Analytic And Probabilistic Number Theory written by Gérald Tenenbaum 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 2015-07-16 with Mathematics categories.

This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. --Mathematical Reviews

Probabilistic Number Theory Ii

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Author : P.D.T.A. Elliott
language : en
Publisher: Springer
Release Date : 1980-03-03

Probabilistic Number Theory Ii written by P.D.T.A. Elliott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-03-03 with Mathematics categories.

In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. The methods involve a synthesis of Probability and Number Theory; sums of independent infinitesimal random variables playing an important role. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;; z {3 (x) ) converge weakly; (see Notation). In contrast to volume one we allow {3(x) to become unbounded with x. In particular, we investigate to what extent one can simulate the behaviour of additive arithmetic functions by that of sums of suit ably defined independent random variables. This fruiful point of view was intro duced in a 1939 paper of Erdos and Kac. We obtain their (now classical) result in Chapter 12. Subsequent methods involve both Fourier analysis on the line, and the appli cation of Dirichlet series. Many additional topics are considered. We mention only: a problem of Hardy and Ramanujan; local properties of additive arithmetic functions; the rate of convergence of certain arithmetic frequencies to the normal law; the arithmetic simulation of all stable laws. As in Volume I the historical background of various results is discussed, forming an integral part of the text. In Chapters 12 and 19 these considerations are quite extensive, and an author often speaks for himself.

Introduction To Analytic And Probabilistic Number Theory

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Author : Gérald Tenenbaum
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-26

Introduction To Analytic And Probabilistic Number Theory written by Gérald Tenenbaum and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.

This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. —Mathematical Reviews

Analytic And Probabilistic Methods In Number Theory

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Author : E. Laurincikas
language : en
Publisher: Walter de Gruyter
Release Date : 2012-02-14

Analytic And Probabilistic Methods In Number Theory written by E. Laurincikas 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 2012-02-14 with Mathematics categories.

Arithmetic Functions And Integer Products

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Author : Peter D. Elliott
language : en
Publisher:
Release Date : 1984-11-20

Arithmetic Functions And Integer Products written by Peter D. Elliott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-11-20 with categories.