Multiplicative Number Theory

Buch | Hardcover
182 Seiten
2000 | 3rd ed. 2000
Springer-Verlag New York Inc.
978-0-387-95097-6 (ISBN)

Lese- und Medienproben

Multiplicative Number Theory - Harold Davenport
64,15 inkl. MwSt
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 Pólya-Vinogradov Inequality.- Further Prime Number Sums.

Reihe/Serie Graduate Texts in Mathematics ; 74
Überarbeitung H.L. Montgomery
Zusatzinfo XIV, 182 p.
Verlagsort New York, NY
Sprache englisch
Maße 156 x 234 mm
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Naturwissenschaften Physik / Astronomie
ISBN-10 0-387-95097-4 / 0387950974
ISBN-13 978-0-387-95097-6 / 9780387950976
Zustand Neuware
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