Davenport H. Multiplicative Number Theory

2nd. edition. — Springer, 1980. — xiv, 177 p. — (Graduate Texts in Mathematics, 74). — ISBN: 978-1-4757-5929-7, 978-1-4757-5927-3.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.Preface to Second Edition
Preface to First EditionNotation
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-Functions
Properties of the Г Function
Integral Functions of Order 1
The Infinite Products for ζ(s) and ζ(s, ψ)
A Zero-Free Region for ζ(s)
Zero-Free Regions for L(s, χ)
The Number N(T)
The Number N(T, χ)
The Explicit Formula for ψ(x)
The Prime Number Theorem
The Explicit Formula for ψ(x, χ)
The Prime Number Theorem for Arithmetic Progressions (I)
Siegel's Theorem
The Prime Number Theorem for Arithmetic Progressions (II)
The Pόlya-Vinogradov Inequality
Further Prime Number Sums
An Exponential Sum Formed with Primes
Sums of Three Primes
The Large Sieve
Bombieri's Theorem
An Average Result
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