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Softcover ISBN:  9780821846018 
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Softcover ISBN:  9780821846018 
Product Code:  COLL/7 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470431570 
Product Code:  COLL/7.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Softcover ISBN:  9780821846018 
eBook ISBN:  9781470431570 
Product Code:  COLL/7.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $112.50 $85.50 
AMS Member Price:  $100.00 $76.00 

Book DetailsColloquium PublicationsVolume: 7; 1927; 180 ppMSC: Primary 11
The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the Bôcher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, elliptic and theta functions, Bernoulli numbers and functions, and the foundations of mathematics.
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

Introduction

Chapter I. Varieties of algebra useful in algebraic arithmetic

Chapter II. The algebra $\mathcal \{B\}$ of parity

Chapter III. The algebraic arithmetic of multiply periodic functions

Chapter IV. Applications of the algebras $\mathcal \{C, D\}$

Chapter V. Arithmetical structure


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The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the Bôcher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, elliptic and theta functions, Bernoulli numbers and functions, and the foundations of mathematics.
Graduate students and research mathematicians interested in number theory.

Chapters

Introduction

Chapter I. Varieties of algebra useful in algebraic arithmetic

Chapter II. The algebra $\mathcal \{B\}$ of parity

Chapter III. The algebraic arithmetic of multiply periodic functions

Chapter IV. Applications of the algebras $\mathcal \{C, D\}$

Chapter V. Arithmetical structure