Arithmetic Functions
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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.
Arithmetical Functions
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Author : Wolfgang Schwarz
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-10
Arithmetical Functions written by Wolfgang Schwarz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-10 with Mathematics categories.
Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis.
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.
Various Arithmetic Functions And Their Applications
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Author : Octavian Cira
language : en
Publisher: Infinite Study
Release Date :
Various Arithmetic Functions And Their Applications written by Octavian Cira and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, Romania). This book was born from the collaboration of the two authors, which started in 2013. The first common work was the volume "Solving Diophantine Equations", published in 2014. The contribution of the authors can be summarized as follows: Florentin Smarandache came with his extraordinary ability to propose new areas of study in number theory, and Octavian Cira - with his algorithmic thinking and knowledge of Mathcad.
Arithmetical Functions
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Author : Komaravolu Chandrasekharan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetical Functions written by Komaravolu Chandrasekharan 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 plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. My Introduction to Analytic Number Theory has appeared in the meanwhile, and this book may be looked upon as a sequel. It presupposes only a modicum of acquaintance with analysis and number theory. The arithmetical functions considered here are those associated with the distribution of prime numbers, as well as the partition function and the divisor function. Some of the problems posed by their asymptotic behaviour form the theme. They afford a glimpse of the variety of analytical methods used in the theory, and of the variety of problems that await solution. I owe a debt of gratitude to Professor Carl Ludwig Siegel, who has read the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the manuscript and correcting the proofs. K. Chandrasekharan July 1970 Contents Chapter I The prime number theorem and Selberg's method § 1. Selberg's fonnula . . . . . . 1 § 2. A variant of Selberg's formula 6 12 § 3. Wirsing's inequality . . . . . 17 § 4. The prime number theorem. .
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.
Arithmetic Functions
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Author : J. Sándor
language : en
Publisher:
Release Date : 2021
Arithmetic Functions written by J. Sándor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Arithmetic functions categories.
"This monograph is devoted to arithmetic functions, an area of number theory. Arithmetic functions are very important in many parts of theoretical and applied sciences, and many mathematicians have devoted great interest in this field. One of the interesting features of this book is the introduction and study of certain new arithmetic functions that have been considered by the authors separately or together, and their importance is shown in many connections with the classical arithmetic functions or in their applications to other problems"--
On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions
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Author : Peter D. T. A. Elliott
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
On The Correlation Of Multiplicative And The Sum Of Additive Arithmetic Functions written by Peter D. T. A. Elliott 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 1994 with Mathematics categories.
The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.
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.
