» Multiplicative Number Theory I: Classical Theory (Cambridge Studies in Advanced Mathematics)

Multiplicative Number Theory I: Classical Theory (Cambridge Studies in Advanced Mathematics) Reviews

Customer Rating:
Summary: comprehensive survey of prime number theory
Comment: Multiplicative number theory deals primarily with the distribution of the prime numbers, but also with the asymptotic behavior of prime-related functions such as the number-of-divisors function. The present work deals with the classical theory in the sense that most of the results were known before 1960. Most of the items covered are part of analytic number theory and the theory of the Riemann zeta function and the L-functions. In addition to the analytic theory the book includes classical estimates of Dirichlet, Chebyshev, and Mertens, as well as some coverage of combinatorial sieves and the Selberg sieve. A second volume is planned that will focus on more delicate estimates, exponential sums, and sieve methods.

The unique feature of the book is its exercises: they cover hundreds of research results (with references), usually just stated but sometimes with hints or a step by step breakdown. The body of the text follows the mainstream and only hits the main results, but gives the student enough background to work on the exercises.

The book is clearly written and includes enough background information to be used for individual study. Some earlier works that have a similar flavor but are less comprehensive are A. E. Ingham's The Distribution of Prime Numbers (Cambridge Mathematical Library) and Harold Davenport's Multiplicative Number Theory

---