Arithmetic Functions And Integer Products
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Arithmetic Functions And Integer Products
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Author : P.D.T.A. Elliott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetic Functions And Integer Products 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.
Every positive integer m has a product representation of the form where v, k and the ni are positive integers, and each Ei = ± I. A value can be given for v which is uniform in the m. A representation can be computed so that no ni exceeds a certain fixed power of 2m, and the number k of terms needed does not exceed a fixed power of log 2m. Consider next the collection of finite probability spaces whose associated measures assume only rational values. Let hex) be a real-valued function which measures the information in an event, depending only upon the probability x with which that event occurs. Assuming hex) to be non negative, and to satisfy certain standard properties, it must have the form -A(x log x + (I - x) 10g(I -x». Except for a renormalization this is the well-known function of Shannon. What do these results have in common? They both apply the theory of arithmetic functions. The two widest classes of arithmetic functions are the real-valued additive and the complex-valued multiplicative functions. Beginning in the thirties of this century, the work of Erdos, Kac, Kubilius, Turan and others gave a discipline to the study of the general value distribution of arithmetic func tions by the introduction of ideas, methods and results from the theory of Probability. I gave an account of the resulting extensive and still developing branch of Number Theory in volumes 239/240 of this series, under the title Probabilistic Number Theory.
Arithmetic Functions And Integer Products
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Author : Peter D. T. A. Elliott
language : en
Publisher:
Release Date : 1985
Arithmetic Functions And Integer Products written by Peter D. T. A. Elliott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Arithmetic functions categories.
Classical Theory Of Arithmetic Functions
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Author : R Sivaramakrishnan
language : en
Publisher: Routledge
Release Date : 2018-10-03
Classical Theory Of Arithmetic Functions written by R Sivaramakrishnan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
The Theory Of Arithmetic Functions
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Author : Anthony A. Gioia
language : en
Publisher: Springer
Release Date : 2006-11-15
The Theory Of Arithmetic Functions written by Anthony A. Gioia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Introduction To Arithmetical Functions
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Author : Paul J. McCarthy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Arithmetical Functions written by Paul J. McCarthy 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.
The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.
Abstract Analytic Number Theory
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Author : Knopfmacher
language : en
Publisher: Newnes
Release Date : 2009-02-04
Abstract Analytic Number Theory written by Knopfmacher and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-04 with Technology & Engineering categories.
North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.
Fundamental Number Theory With Applications
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Author : Richard A. Mollin
language : en
Publisher: CRC Press
Release Date : 1997-09-10
Fundamental Number Theory With Applications written by Richard A. Mollin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-10 with Mathematics categories.
Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to cryptography factoring primality testing complexity analysis computer arithmetic computational number theory Fundamental Number Theory with Applications also covers: Carmichael numbers Dirichlet products Jacobsthal sums Mersenne primes perfect numbers powerful numbers self-contained numbers Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material. Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.
Certain Number Theoretic Episodes In Algebra Second Edition
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Author : R Sivaramakrishnan
language : en
Publisher: CRC Press
Release Date : 2019-03-19
Certain Number Theoretic Episodes In Algebra Second Edition written by R Sivaramakrishnan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-19 with Mathematics categories.
The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Products Of Random Variables
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Author : Janos Galambos
language : en
Publisher: CRC Press
Release Date : 2004-07-20
Products Of Random Variables written by Janos Galambos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-20 with Mathematics categories.
Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. It uses entirely probabilistic arguments in actualizing the potential of the asymptotic theory of products of independent random variab
Analytic Number Theory For Undergraduates
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Author : Heng Huat Chan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-04-21
Analytic Number Theory For Undergraduates written by Heng Huat Chan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-21 with Mathematics categories.
This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression. The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.
