Riemann's Zeta Function

By: Edwards,H.MMaterial type: TextTextSeries: 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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Item type Current library Collection Call number Status Date due Barcode Item holds
Reference Books Reference Books Main Library
Reference 		Reference 515.56 EDW (Browse shelf(Opens below)) Available 009829
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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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