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Multiplicative Number Theory Harold Davenport

Multiplicative Number Theory von Harold Davenport

Multiplicative Number Theory Harold Davenport

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Zusammenfassung

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.

Multiplicative Number Theory Zusammenfassung

Multiplicative Number Theory Harold Davenport

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.

Multiplicative Number Theory Bewertungen

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. Davenports 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)

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 Polya-Vinogradov Inequality.- Further Prime Number Sums.

Zusätzliche Informationen

GOR012906654
9780387950976
0387950974
Multiplicative Number Theory Harold Davenport
Harold Davenport
Graduate Texts in Mathematics
Gebraucht - Sehr Gut
Gebundene Ausgabe
Springer-Verlag New York Inc.
2000-10-31
182
N/A
Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
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