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Riemann's Zeta Function by H M. Edwards

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eBay item number:166853425875
Last updated on Aug 02, 2024 22:04:54 PDTView all revisionsView all revisions

Item specifics

Condition
Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See the ...
EAN
9780486417400
UPC
9780486417400
ISBN
9780486417400
MPN
N/A
Subject Area
Mathematics
Publication Name
Riemann's Zeta Function
Publisher
Dover Publications, Incorporated
Item Length
8.7 in
Subject
Functional Analysis, Number Theory
Publication Year
2001
Series
Dover Books on Mathematics Ser.
Type
Textbook
Format
Trade Paperback
Language
English
Item Height
0.7 in
Author
H. M. Edwards
Features
Large Type
Item Weight
14.4 Oz
Item Width
5.7 in
Number of Pages
336 Pages

About this product

Product Identifiers

Publisher
Dover Publications, Incorporated
ISBN-10
0486417409
ISBN-13
9780486417400
eBay Product ID (ePID)
1825277

Product Key Features

Number of Pages
336 Pages
Publication Name
Riemann's Zeta Function
Language
English
Publication Year
2001
Subject
Functional Analysis, Number Theory
Features
Large Type
Type
Textbook
Author
H. M. Edwards
Subject Area
Mathematics
Series
Dover Books on Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Height
0.7 in
Item Weight
14.4 Oz
Item Length
8.7 in
Item Width
5.7 in

Additional Product Features

Intended Audience
College Audience
LCCN
2001-028010
Dewey Edition
21
Illustrated
Yes
Dewey Decimal
515/.56
Table Of Content
Preface; Acknowledgments Chapter 1. Riemann''s Paper 1.1 The Historical Context of the Paper 1.2 The Euler Product Formula 1.3 The Factorial Function 1.4 The Function zeta (s) 1.5 Values of zeta (s) 1.6 First Proof of the Functional Equation 1.7 Second Proof of the Functional Equation 1.8 The Function xi (s) 1.9 The Roots rho of xi 1.10 The Product Representation of xi (s) 1.11 The Connection between zeta (s) and Primes 1.12 Fourier Inversion 1.13 Method for Deriving the Formula for J(x) 1.14 The Principal Term of J(x) 1.15 The Term Involving the Roots rho 1.16 The Remaining Terms 1.17 The Formula for pi (x) 1.18 The Density dJ 1.19 Questions Unresolved by Riemann Chapter 2. The Product Formula for xi 2.1 Introduction 2.2 Jensen''s Theorem 2.3 A Simple Estimate of absolute value of xi (s) 2.4 The Resulting Estimate of the Roots rho 2.5 Convergence of the Product 2.6 Rate of Growth of the Quotient 2.7 Rate of Growth of Even Entire Functions 2.8 The Product Formula for xi Chapter 3. Riemann''s Main Formula 3.1 Introduction 3.2 Derivation of von Mangoldt''s formula for psi (x) 3.3 The Basic Integral Formula 3.4 The Density of the Roots 3.5 Proof of von Mangoldt''s Formula for psi (x) 3.6 Riemann''s Main Formula 3.7 Von Mangoldt''s Proof of Reimann''s Main Formula 3.8 Numerical Evaluation of the Constant Chapter 4. The Prime Number Theorem 4.1 Introduction 4.2 Hadamard''s Proof That Re rho infinity and the Location of Its Zeros 9.1 Introduction 9.2 Lindelöf''s Estimates and His Hypothesis 9.3 The Three Circles Theorem 9.4 Backlund''s Reformulation of the Lindelöf Hypothesis 9.5 The Average Value of S(t) Is Zero 9.6 The Bohr-Landau Theorem 9.7 The Average of absolute value zeta(s) superscript 2 9.8 Further Results. Landau''s Notation o, O Chapter 10. Fourier Analysis 10.1 Invariant Operators on R superscript + and Their Transforms 10.2 Adjoints and Their Transforms 10.3 A Self-Adjoint Operator with Transform xi (s) 10.4 The Functional Equation 10.5 2 xi (s)/s(s - 1) as a Transform 10.6 Fourier Inversion 10.7 Parseval''s Equation 10.8 The Values of zeta (-n) 10.9 Möbius Inversion 10.10 Ramanujan''s Formula Chapter 11. Zeros on the Line 11.1 Hardy''s Theorem 11.2 There Are at Least KT Zeros on the Line 11.3 There Are at Least KT log T Zeros on the Line 11.4 Proof of a Lemma Chapter 12. Miscellany 12.1 The Riemann Hypothesis and the Growth of M(x) 12.2 The Riemann Hypothesis and Farey Series 12.3 Denjoy''s Probabilistic Interpretation of the Riemann Hypothesis 12.4 An Interesting False Conjecture 12.5 Transforms with Zeros on the Line 12.6 Alternative Proof of the Integral Formula 12.7 Tauberian Theorems 12.8 Chebyshev''s Identity 12.9 Selberg''s Inequality 12.10 Elementary Proof of the Prime Number Theorem 12.11 Other Zeta Functions. Weil''s Theorem Appendix. On the Number of Primes Less Than a Given Magnitude (By Bernhard Riemann) References; Index
Edition Description
Large Type / large print edition
Synopsis
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 Vall e 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. This inexpensive edition of Edwards' superb high-level study will be welcomed by students and mathematicians. Mathematically inclined general readers will likewise value this influential classic., Superb study of one of the most influential classics in mathematics examines the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude," and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics., 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. This inexpensive edition of Edwards' superb high-level study will be welcomed by students and mathematicians. Mathematically inclined general readers will likewise value this influential classic.
LC Classification Number
QA241.E39

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Most relevant reviews

  • Jumping Jack?

    The Riemann's Zeta Function in itself is already an advance topic, and this book adds to the zeta function's difficulty by not keeping the reader on one train-of-thought following another. Instead the author jumps from one theme to another (sometimes it jumps math themes from different eras...). The reader would need to have foreknowledge (very good knowledge) of Number Theory history (who developed what theory when or who built theorems upon the works of whom) in order to follow the jumps Mr. H. Edwards makes. Unfortunately, this book is NOT for the undergraduate.