Multiplicative Number Theory [Hardcover]

The new edition of this thorough examination of the distribution of prime numbers in arithmetic progressions offers many revisions and corrections as well as a new section recounting recent works in the field. The book covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions and the theorem of Siegel. It also presents a simplified, improved version of the large sieve method.

From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- The Distribution of the Primes.- Riemann's Memoir.- The Functional Equation of the L Function.- Properties of the Gamma Function.- Integral Functions of Order 1.- The Infinite Products for xi(s) and xi(s,Zero-Free Region for zeta(s).- Zero-Free Regions for L(s, chi).- The Number N(T).- The Number N(T, chi).- The explicit Formula for psi(x).- The Prime Number Theorem.- The Explicit Formula for psi(x,chi).- The Prime Number Theorem for Arithmetic Progressions (I).- Siegel's Theorem.- The Prime Number Theorem for Arithmetic Progressions (II).- The P?lya-Vinogradov Inequality.- Further Prime Number Sums.

From the reviews of the third edition:

The book under review is one of the most important references in the multiplicative number theory, as its title mentions exactly. & Davenports book covers most of the important topics in the theory of distribution of primes and leads the reader to serious research topics & . is very well written. & is useful for graduate students, researchers and for professors. It is a very good text source specially for graduate levels, but even is fruitful for undergraduates. (Mehdi Hassani, MathDL, July, 2008)

This book thoroughly examines the distribution of prime numlƒ/