Includes bibliographical references (pages 375-377) and index.
Contents
Sums and differences -- Products and divisibility -- Order and magnitude -- Averages -- Calculus -- Primes -- Series -- Basel problem -- Euler's product -- Complex numbers -- The Riemann zeta function -- Symmetry -- Explicit formula -- Modular arithmetic -- Pell's equation -- Elliptic curves -- Analytic theory of algebraic numbers.
Summary
"This undergraduate introduction to analytic number theory develops analytic skills in the course of a study of ancient questions on polygonal numbers, perfect numbers, and amicable pairs. The question of how the primes are distributed among all integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeros of his function and the significance of the Riemann Hypothesis."--Jacket.