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Multiplicative Number Theory

Buch von Harold Davenport

71107070
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  • Details
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Details
Artikel-Nr.:
71107070
Im Sortiment seit:
01.08.2012
Erscheinungsdatum:
31.10.2000
Medium:
Buch
Einband:
Gebunden
Auflage:
3rd ed. 2000
Autor:
Davenport, Harold
Bearbeitung:
Montgomery, H. L.
Verlag:
Springer New York
Springer US
Sprache:
Englisch
Schlagworte:
Rubrik:
Mathematik
Wahrscheinlichkeitstheorie
Seiten:
200
Informationen:
HC runder Rücken kaschiert
Gewicht:
471 gr
Beschreibung
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.
Information
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.
Inhaltsverzeichnis
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.
Lesekritik
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)
Bilder