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＜電子ブック＞
The Riemann Hypothesis : A Resource for the Afficionado and Virtuoso Alike / edited by Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
(CMS Books in Mathematics, Ouvrages de mathématiques de la SMC. ISSN:21974152)

版	1st ed. 2008.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XIV, 533 p : online resource
著者標目	Borwein, Peter editor Choi, Stephen editor Rooney, Brendan editor Weirathmueller, Andrea editor SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Mathematics LCSH:History FREE:Number Theory FREE:History of Mathematical Sciences
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-0-387-72126-2

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