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.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

• Introduction
• Varieties of algebra useful in algebraic arithmetic
• The algebra $\mathcal{B}$ of parity
• The algebraic arithmetic of multiply periodic functions
• Applications of the algebras $\mathcal{C, D}$
• Arithmetical structure
• Index