Multiplicative Number Theory
3rd Edition
Published on 31. October 2000
Book
Hardback
XIV, 182 pages
978-0-387-95097-6 (ISBN)
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 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.
Reviews / Votes
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. . Davenport's 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)
More details
Series
Edition
3rd ed. 2000
Language
English
Place of publication
New York
United States
Target group
Primary & secondary/elementary & high school
Graduate
Edition type
New edition
Illustrations
XIV, 182 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 17 mm
Weight
471 gr
ISBN-13
978-0-387-95097-6 (9780387950976)
Schweitzer Classification
Other editions
Previous edition
H. Davenport | Harold Davenport
Multiplicative Number Theory
Book
12/1980
2nd Edition
Springer
€36.14
Article exhausted; check for reprint
Persons
Content
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 Pólya-Vinogradov Inequality.- Further Prime Number Sums.