Multiplicative Number Theory

ISBN-10: 0387950974
ISBN-13: 9780387950976
Edition: 3rd 2000 (Revised)
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Description: This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions, the theorem of Siegel, and  More...

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Book details

List price: $79.95
Edition: 3rd
Copyright year: 2000
Publisher: Springer
Publication date: 10/31/2000
Binding: Hardcover
Pages: 182
Size: 6.00" wide x 9.25" long x 0.50" tall
Weight: 0.880

This book thoroughly examines the distribution of prime numbers in arithmetic progressions. It covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions, the theorem of Siegel, and functional equations of the L-functions and their consequences for the distribution of prime numbers. In addition, a simplified, improved version of the large sieve method is presented. The 3rd edition includes a large number of revisions and corrections as well as a new section with references to more recent work in the field.

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[$$$][3]lya-Vinogradov Inequality
Further Prime Number Sums

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