This text covers material from both the algebraic and analytic disciplines and includes coverage of recent developments, such as the new primality test and other topics of significant interest, which are often omitted from other books at this level. It aims to take readers to a deeper understanding of the patterns of thought that have shaped the modern understanding of number theory.

Klappentext

Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test

Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight

Inhalt

A Brief History of Prime.- Diophantine Equations.- Quadratic Diophantine Equations.- Recovering the Fundamental Theorem of Arithmetic.- Elliptic Curves.- Elliptic Functions.- Heights.- The Riemann Zeta Function.- The Functional Equation of the Riemann Zeta Function.- Primes in an Arithmetic Progression.- Converging Streams.- Computational Number Theory.