The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike / Edition 1

The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike / Edition 1

by Peter Borwein
     
 

ISBN-10: 1441924655

ISBN-13: 9781441924650

Pub. Date: 11/23/2010

Publisher: Springer New York

The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with

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Overview

The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors."

The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers.

This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis.

The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

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Product Details

ISBN-13:
9781441924650
Publisher:
Springer New York
Publication date:
11/23/2010
Series:
CMS Books in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2008
Pages:
533
Sales rank:
847,262
Product dimensions:
6.10(w) x 9.20(h) x 1.30(d)

Table of Contents

to the Riemann Hypothesis.- Why This Book.- Analytic Preliminaries.- Algorithms for Calculating—(s).- Empirical Evidence.- Equivalent Statements.- Extensions of the Riemann Hypothesis.- Assuming the Riemann Hypothesis and Its Extensions ….- Failed Attempts at Proof.- Formulas.- Timeline.- Original Papers.- Expert Witnesses.- The Experts Speak for Themselves.

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