Description
Springer Multiplicative Number Theory by Harold Davenport, Revised by H.L. Montgomery
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._x000D_ Table of contents :- _x000D_
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 Polya-Vinogradov Inequality.- Further Prime Number Sums._x000D_