The Riemann Hypothesis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Riemann Hypothesis write by Peter B. Borwein. This book was released on 2008. The Riemann Hypothesis available in PDF, EPUB and Kindle. 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.
Prime Numbers and the Riemann Hypothesis
Prime Numbers and the Riemann Hypothesis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Prime Numbers and the Riemann Hypothesis write by Barry Mazur. This book was released on 2016-04-11. Prime Numbers and the Riemann Hypothesis available in PDF, EPUB and Kindle. This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Stalking the Riemann Hypothesis
Stalking the Riemann Hypothesis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stalking the Riemann Hypothesis write by Dan Rockmore. This book was released on 2006-05-09. Stalking the Riemann Hypothesis available in PDF, EPUB and Kindle. For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Riemann's Zeta Function
Riemann's Zeta Function - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Riemann's Zeta Function write by Harold M. Edwards. This book was released on 2001-01-01. Riemann's Zeta Function available in PDF, EPUB and Kindle. Superb high-level study of one of the most influential classics in mathematics examines 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. English translation of Riemann's original document appears in the Appendix.
The Riemann Hypothesis and the Roots of the Riemann Zeta Function
The Riemann Hypothesis and the Roots of the Riemann Zeta Function - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Riemann Hypothesis and the Roots of the Riemann Zeta Function write by Samuel W. Gilbert. This book was released on 2009. The Riemann Hypothesis and the Roots of the Riemann Zeta Function available in PDF, EPUB and Kindle. The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function.
