Ebook: Topics from the theory of numbers

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory.

Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including:

* divisibility

* congruences

* the Riemann zeta function

* Diophantine equations and Fermat’s conjecture

* the theory of partitions

Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike.

"In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald."

— Marc Kac

"This book is designed for use in a first course in number theory at the junior or senior level...The author has certainly planned his book well, chosen material that will be stimulating to its intended audience, and carried the project through in such a way that interest seldom flags."

— Mathematical Reviews (Review of First Edition)

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Arithmetic Functions and Integer Products presents an algebraically oriented approach to the theory of additive and multiplicative arithmetic functions. This is a very active theory with applications in many other areas of mathematics, such as functional analysis, probability and the theory of group representations. Elliott's volume gives a systematic account of the theory, embedding many interesting and far-reaching individual results in their proper context while introducing the reader to a very active, rapidly developing field. In addition to an exposition of the theory of arithmetical functions, the book contains supplementary material (mostly updates) to the author's earlier two volumes on probabilistic number theory Preface.- Preface to the First Edition.- Part One. Introduction, Historical Background, and Notations.- Introduction and Historical Background.- Introductory Remarks and Notations.- Part Two. Elementary Number Theory.- Divisibility.- Congruences.- Quadratic Residues.- Arithmetical Functions.- The Theory of Partitions.- Part Three. Topics from Analytic and Algebraic Number Theory.- The Distribution of Primes and the Riemann Zeta Function.- The Prime Number Theorem.- The Arithmetic of Number Fields.- Ideal Theory.- Primes in Arithmetic Professions.- Diophantine Equations.- Fermat's Equation.- Answers to Selected Problems.- Subject Index.- Name Index.- Index of Functions