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Riemann's Zeta Function

By: Edwards,H.MMaterial type: Text

TextSeries: Pure and applied mathematics (Academic Press), 58Publication details: Mineola, NY : Dover Publications, 2001Description: xiii, 315 pagesISBN: 9780486417400; 0486417409 Subject(s): Number theoryDDC classification: 515.56

Contents:

Riemann's Paper -- The Product Formula for xi -- Riemann's Main Formula -- The Prime Number Theorem -- De la Vallee Poussin's Theorem -- Numerical Analysis of the Roots by Euler-Maclaurin Summation -- The Riemann-Siegel Formula -- Large-Scale Computations -- The Growth of Zeta as t -- > infinity and the Location of Its Zeros -- Fourier Analysis -- Zeros on the Line -- Miscellany

Summary: "Bernhard Riemann's eight-page paper entitled "On the Number of Primes Less Than a Given Magnitude" was a landmark publication of 1859 that directly influenced generations of great mathematicians, among them Hadamard, Landau, Hardy, Siegel, Jensen, Bohr, Selberg, Artin, and Hecke. This text, by a noted mathematician and educator, examines and amplifies the paper itself, and traces the developments in theory inspired by it. (An English translation of the original document appears in the Appendix.) Topics include Riemann's main formula, the prime number theorem, de la Vallée Poussin's theorem, numerical analysis of roots by Euler-Maclaurin summation, the Riemann-Siegel formula, largescale computations, Fourier analysis, zeros on the line, the Riemann hypothesis and Farey series, alternative proof of the integral formula, Tauberian theorems, Chebyshev's identity, and other related topics."--Publisher's description.

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Reference Books	Main Library Reference	Reference	515.56 EDW (Browse shelf(Opens below))	Available		009829

Total holds: 0

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Previous	515.43 WIL An introduction to Lebesgue integration and Fourier series	515.5 LEB Special Functions and Their Applications	515.53 BOW Introduction to Bessel Functions	515.56 EDW Riemann's Zeta Function	515.62 SAX Examples in Finite Differences and Numerical Analysis	515.62 SAX Finite Differences and Numerical Analysis: with Appendices on Difference Equations	515.62 SAX Finite Differences and Numerical Analysis	Next

Includes Index

Riemann's Paper --
The Product Formula for xi --
Riemann's Main Formula --
The Prime Number Theorem --
De la Vallee Poussin's Theorem --
Numerical Analysis of the Roots by Euler-Maclaurin Summation --
The Riemann-Siegel Formula --
Large-Scale Computations --
The Growth of Zeta as t --
> infinity and the Location of Its Zeros --
Fourier Analysis --
Zeros on the Line --
Miscellany

"Bernhard Riemann's eight-page paper entitled "On the Number of Primes Less Than a Given Magnitude" was a landmark publication of 1859 that directly influenced generations of great mathematicians, among them Hadamard, Landau, Hardy, Siegel, Jensen, Bohr, Selberg, Artin, and Hecke. This text, by a noted mathematician and educator, examines and amplifies the paper itself, and traces the developments in theory inspired by it. (An English translation of the original document appears in the Appendix.) Topics include Riemann's main formula, the prime number theorem, de la Vallée Poussin's theorem, numerical analysis of roots by Euler-Maclaurin summation, the Riemann-Siegel formula, largescale computations, Fourier analysis, zeros on the line, the Riemann hypothesis and Farey series, alternative proof of the integral formula, Tauberian theorems, Chebyshev's identity, and other related topics."--Publisher's description.

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