Classical Theory Of Arithmetic Functions

Author : R Sivaramakrishnan
Publisher : Routledge
Page : 406 pages
File Size : 44,8 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781351460521

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Classical Theory of Arithmetic Functions by R Sivaramakrishnan Pdf

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 It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs.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

Author : R Sivaramakrishnan
Publisher : Routledge
Page : 205 pages
File Size : 43,8 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781351460514

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Classical Theory of Arithmetic Functions by R Sivaramakrishnan Pdf

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 It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs.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

Author : Hugh L. Montgomery,Robert C. Vaughan
Publisher : Cambridge University Press
Page : 574 pages
File Size : 49,6 Mb
Release : 2007
Category : Mathematics
ISBN : 0521849039

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Multiplicative Number Theory I by Hugh L. Montgomery,Robert C. Vaughan Pdf

A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.

Author : Anthony A. Gioia,Donald L. Goldsmith
Publisher : Unknown
Page : 300 pages
File Size : 50,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662212013

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The Theory of Arithmetic Functions by Anthony A. Gioia,Donald L. Goldsmith Pdf

Author : Paul J. McCarthy
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461386209

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Introduction to Arithmetical Functions by Paul J. McCarthy Pdf

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.

Author : József Sándor,Krassimir Todorov Atanassov
Publisher : Nova Science Publishers
Page : 253 pages
File Size : 46,7 Mb
Release : 2021
Category : Mathematics
ISBN : 1536196770

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Arithmetic Functions by József Sándor,Krassimir Todorov Atanassov Pdf

"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"--

Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 46,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475738452

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Additive Number Theory The Classical Bases by Melvyn B. Nathanson Pdf

[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

Author : J. Sándor,Krassimir Todorov Atanassov
Publisher : Unknown
Page : 0 pages
File Size : 40,5 Mb
Release : 2021
Category : Arithmetic functions
ISBN : 1536194751

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Arithmetic Functions by J. Sándor,Krassimir Todorov Atanassov Pdf

"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"--

Author : Themistocles M. Rassias,Panos M. Pardalos
Publisher : Springer
Page : 781 pages
File Size : 48,7 Mb
Release : 2014-09-17
Category : Mathematics
ISBN : 9781493911066

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Mathematics Without Boundaries by Themistocles M. Rassias,Panos M. Pardalos Pdf

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.

Author : Peter D. T. A. Elliott
Publisher : Unknown
Page : 488 pages
File Size : 50,9 Mb
Release : 1985
Category : Arithmetic functions
ISBN : UCAL:B4407299

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Arithmetic Functions and Integer Products by Peter D. T. A. Elliott Pdf

Author : Wolfgang Schwarz,Jürgen Spilker
Publisher : Cambridge University Press
Page : 392 pages
File Size : 51,9 Mb
Release : 1994-03-10
Category : Mathematics
ISBN : 0521427258

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Arithmetical Functions by Wolfgang Schwarz,Jürgen Spilker Pdf

Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis.

Author : L J P Kilford
Publisher : World Scientific Publishing Company
Page : 252 pages
File Size : 51,5 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9781783265473

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Modular Forms by L J P Kilford Pdf

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it. This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

Author : P.D.T.A. Elliott
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299929

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Probabilistic Number Theory II by P.D.T.A. Elliott Pdf

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.

Author : Matti Jutila,Tauno Metsänkylä
Publisher : Walter de Gruyter
Page : 340 pages
File Size : 52,5 Mb
Release : 2014-01-02
Category : Mathematics
ISBN : 9783110870923

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Number Theory by Matti Jutila,Tauno Metsänkylä Pdf

These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.

Author : J. Sándor,B. Crstici
Publisher : Springer Science & Business Media
Page : 637 pages
File Size : 46,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9781402025464

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Handbook of Number Theory II by J. Sándor,B. Crstici Pdf

This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.