61. Unsolved Math Problem Turns 150 – SciTechBlog - CNN.com Blogs Nov 18, 2009 Proposed by Bernhard Riemann in 1859, the Riemann Hypothesis deals with prime numbers. You may recall that a prime number is a positive http://scitech.blogs.cnn.com/2009/11/18/unsolved-math-problem-turns-150/

62. Riemann Hypothesis - Wikipedia Mar 15, 2009 In mathematics, the Riemann hypothesis, due to Bernhard Riemann (1859), is a conjecture about the distribution of the zeros of the Riemann http://www.scribd.com/doc/13289163/Riemann-Hypothesis-Wikipedia

63. Riemann Summary Theory of functions, non-Euclidian geometry, relativity theory, Famous for the Riemann hypothesis about the behavior of zeros of the Riemann zeta function, which he showed determines the distribution of prime numbers. http://turnbull.dcs.st-and.ac.uk/history/Mathematicians/Riemann.html

Georg Friedrich Bernhard Riemann Click the picture above to see four larger pictures Riemann 's ideas concerning geometry of space had a profound effect on the development of modern theoretical physics. He clarified the notion of integral by defining what we now call the Riemann integral. Full MacTutor biography [Version for printing] List of References (18 books/articles) Some Quotations Mathematicians born in the same country Show birthplace location Honours awarded to Bernhard Riemann (Click below for those honoured in this way) Fellow of the Royal Society Lunar features Crater Riemann Popular biographies list Number 40 Other Web sites Encyclopaedia Britannica NNDB David R Wilkins European Mathematical Society (Riemann's papers) Luneburg Germany (in German) GMFW in German) Mathematical Genealogy Project Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR © September 1998 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Riemann.html

64. [0807.0090] A Proof Of The Riemann Hypothesis by XJ Li 2008 - Related articles http://arxiv.org/abs/0807.0090

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: Source Current browse context: math.NT new recent Change to browse by: math NASA ADS 14 blog links what is this? Bookmark what is this? Mathematics > Number Theory Title: A proof of the Riemann hypothesis Authors: Xian-Jin Li (Submitted on 1 Jul 2008 ( ), last revised 6 Jul 2008 (this version, v4)) Abstract: This paper has been withdrawn by the author, due to a mistake on page 29. Comments: withdrawn by author, due to mistake on page 29 Subjects: Number Theory (math.NT) MSC classes: Cite as: arXiv:0807.0090v4 [math.NT] Submission history From: Xian-Jin Li [ view email Tue, 1 Jul 2008 19:43:13 GMT (20kb) Wed, 2 Jul 2008 11:05:52 GMT (20kb) Thu, 3 Jul 2008 03:44:03 GMT (20kb) Sun, 6 Jul 2008 12:40:00 GMT (0kb,I) Which authors of this paper are endorsers? Link back to: arXiv form interface contact

65. Riemann Hypothesis The Riemann Hypothesis states conjectures that all nontrivial roots of the Riemann Zeta Function occur on the critical line on the argand plane Re(z) = 1/2, that is, the real http://everything2.com/index.pl?node_id=778126&displaytype=printable&las

66. THE WORLD QUESTION CENTER 2009 — Page 3 The proof of the Riemann Hypothesis involves the zeta function, The proof of Riemann s Hypothesis will have profound consequences for the theory of http://www.edge.org/q2009/q09_3.html

Home About Edge Features Edge Editions ... next WHAT WILL CHANGE EVERYTHING? CONTRIBUTORS Jesse Bering Freeman Dyson Richard Foreman Haim Harari ... THOMAS METZINGER Philosopher, Wissenschaftskolleg zu Berlin (Institute for Advanced Study); Author, The Ego Tunnel SOUL-TRAVEL FOR SELFLESS BEINGS John Brockman points out that new technology leads not only to new ways of perceiving ourselves, but also to a process he calls "recreating ourselves." Could this become true in an even deeper and more radical way than through gene-technology? The answer is yes. It is entirely plausible that we may one day directly control virtual models of our own bodies directly with our brain. In 2007, I first experienced taking control of a computer-generated whole-body model myself. It took place in a virtual reality lab where my own physical motions were filmed by 18 cameras picking up signals from sensors attached to my body. Over the past two years, different research groups in Switzerland, England, Germany and Sweden have demonstrated how, in a passive condition, subjects can consciously identify with the content of a computer-generated virtual body representation, fully re-locating the phenomenal sense of self into an artificial, visual model of their body.

67. Prime Obsession The book is an account, both historical and mathematical, of the Riemann Hypothesis, a famous unsolved problem in mathematics. http://www.johnderbyshire.com/Books/Prime/page.html

Prime Obsession Navigation My Home Page Books main page Blog Prime Obsession was published in hardback (upper image at left) in April 2003 by Joseph Henry Press of Washington D.C. A paperback edition (lower image) was brought out in May 2004 by Plume, a division of Penguin Books, U.S.A. (New York). The book is an account, both historical and mathematical, of the Riemann Hypothesis, a famous unsolved problem in mathematics. Prime Obsession was surprisingly well received for a book of that kind. It has been translated into many languages, including, to my certain knowledge, German, Italian, Greek, Spanish, Czech, Polish, and Russian . There are also translations in all the big three East Asian languages: Chinese Japanese , and Korean In January 2007, Prime Obsession was awarded the Euler Book Prize by the Mathematical Association of America. The prize is awarded for the best popular exposition in book form of a mathematical topic. here here here Top of this page

68. Riemann Hypothesis - Wolfram Demonstrations Project The Riemann hypothesis is one of today's most important problems in mathematics. The hypothesis states that all of the nontrivial zeros of the Riemann zeta function are located http://demonstrations.wolfram.com/RiemannHypothesis/

69. Proof Of The Riemann Hypothesis? « Not Even Wrong Jul 2, 2008 Last night a preprint by XianJin Li appeared on the arXiv, claiming a proof of the Riemann Hypothesis. Preprints claiming such a proof have http://www.math.columbia.edu/~woit/wordpress/?p=707

70. Count Him In - Washingtonpost.com May 23, 2005 The Riemann hypothesis is one of the Seven Millennium Problems posed by the Clay Mathematics Institute in Cambridge, Mass., and whoever http://www.washingtonpost.com/wp-dyn/content/article/2005/05/22/AR2005052201225.

71. [0706.2840v2] A Counterexample To Havil's "Reformulation" Of The Riemann Hypothe Oct 18, 2010 It corrects a mistake in the reformulation of the Riemann Hypothesis in J. Havil s book Gamma Exploring Euler s Constant. http://arxiv4.library.cornell.edu/abs/0706.2840v2

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF only Current browse context: math.NT new recent Change to browse by: math math.GM NASA ADS Bookmark what is this? Mathematics > Number Theory Title: A Counterexample to Havil's "Reformulation" of the Riemann Hypothesis Authors: Jonathan Sondow (Submitted on 19 Jun 2007 ( ), last revised 18 Oct 2010 (this version, v2)) Abstract: This is an elementary note. It corrects a mistake in the reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant. Comments: 2 pages, clarified the last section Subjects: Number Theory (math.NT) ; General Mathematics (math.GM) MSC classes: Cite as: arXiv:0706.2840v2 [math.NT] Submission history From: Jonathan Sondow [ view email Tue, 19 Jun 2007 17:13:32 GMT (13kb) Mon, 18 Oct 2010 04:44:05 GMT (670kb) Which authors of this paper are endorsers? Link back to: arXiv form interface contact

72. Riemann Hypothesis The real part (red) and imaginary part (blue) of the Riemann zetafunction along the critical line Re(s) = 1/2. You can see the first non-trivial zeros at Im(s) = 14.135 http://english.turkcebilgi.com/Riemann hypothesis

EnglishInfo Search Türkçe Home Information Translation ... Riemann hypothesis Information about Riemann hypothesis Riemann hypothesis Information about Riemann hypothesis Double click any English word, to find Turkish meaning There is also the Riemann hypothesis for curves over finite fields The real part (red) and imaginary part (blue) of the critical line Re( s ) = 1/2 of the Riemann zeta-function. You can see the first non-trivial zeros at Im( s ) = ±14.135, ±21.022 and ±25.011. A Value Graph of zeta, that is, Re(zeta) vs. Im(zeta), along the critical line s it + 1/2, with t running from to 34 The Riemann hypothesis (also called the Riemann zeta-hypothesis ), first formulated by Bernhard Riemann in 1859, is one of the most famous and important unsolved problems in mathematics . It has been an open question for well over a century, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs. The Riemann hypothesis (RH) is a conjecture about the distribution of the zero s of the Riemann zeta-function s ). The Riemann zeta-function is defined for all

73. Bookslut | The Music Of The Primes By Marcus Du Sautoy The Riemann Hypothesis has never gained as much public attention as other unsolved mathematical problems, presumably because it is not only abstract, http://www.bookslut.com/nonfiction/2003_10_000758.php

@import "/c/style.css"; @import "/c/style.css"; Bookslut Home Features Reviews Columns ... Advertise October 2003 David Harris nonfiction The Music of the Primes by Marcus du Sautoy In 1900, the great German mathematician David Hilbert presented a lecture to the International Congress of Mathematicians in which he outlined a program for the development of mathematics. His program was defined by a set of 23 unsolved mathematical problems that represented the most significant gaps in mathematical knowledge at the time. A century later, only one of the problems remains completely unsolved. The problem appeared in a 10-page paper by Bernhard Riemann, published in 1859. The Riemann Hypothesis, as it is now known, makes claims about the nature and distribution of prime numbers, the building blocks of mathematics. It has fundamental importance to many areas of mathematics but also impacts on the everyday world. It is interesting and important enough that there is $1 million bounty for its solution, offered by the Clay Mathematics Institute. Information security currently rests on the apparent difficulty of factoring large numbers into primes. If the Riemann Hypothesis is proven, the proof may provide a quick way to factor numbers, and hence crack all of the major cryptographic systems currently in use. For this reason, groups ranging from banks to national security agencies are investing heavily in the abstract and abstruse pure mathematics behind the Riemann Hypothesis.

74. THE RIEMANN HYPOTHESIS AND INVERSE SPECTRAL PROBLEMS FOR FRACTAL Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://jlms.oxfordjournals.org/content/52/1/15.full.pdf

75. Riemann Hypothesis | Facebook Welcome to the Facebook Community Page about Riemann hypothesis, a collection of shared knowledge concerning Riemann hypothesis. http://www.facebook.com/pages/Riemann-hypothesis/109579369061011?v=stream

76. Prime Numbers And Twin Primes - National Curve Bank Thus, the distribution of primes is closely related to one of the most renowned unsolved questions in mathematics, the Riemann hypothesis, which concerns an http://curvebank.calstatela.edu/prime/prime.htm

Back to . . . . Curve Bank Home NCB Deposit # 19 Chris K. Caldwell Department of Mathematics University of Tennessee, Martin Martin, Tennessee caldwell@utm.edu Prime Numbers Twin Primes From ( IX, 20) of the Elements. Math in the news: Are there an infinite number of pairs of "twin primes?" For the student . . . . Background . . . . Twin primes are pairs of prime numbers that only differ by two. Examples: 3 and 5 5 and 7 11 and 13 17 and 19 29 and 31 41 and 43 59 and 61 Until recently, it had been conjectured that there are infinitely many twin primes. If the probability of a random integer n and the integer n+2 being prime were statistically independent events, then it would follow from the prime number theorem that there are about n/(log n) twin primes less than or equal to n. These probabilities are not independent. A famous team of British mathematicians - hmm, another pair so to speak, Hardy and Littlewood, conjectured that the correct estimate should be the following: But conjecture is not a proof. Recently, in March 2003, a new team of mathematicians - Dan Goldston of San Jose State University in California and Cem Yalcin Yildirim of Bogazici University in Istanbul, Turkey - announced they had at least made progress in proving the suspicion that pairs of primes keep going off to infinity.

77. LRB · Karl Sabbagh · The Strange Case Of Louis De Branges Two years ago I wrote a book about the Riemann Hypothesis (for an account of the hypothesis see A.W. Moore s article in this issue). The proof of it is http://www.lrb.co.uk/v26/n14/karl-sabbagh/the-strange-case-of-louis-de-branges

skip navigation London Review of Books home page from the latest issue site map ... Karl Sabbagh RELATED ARTICLES 13 April 2000 Lorraine Daston Why statistics tend not only to describe the world but to change it 11 September 2003 Steven Shapin The Entrepreneurial University 10 June 2010 Cathy Gere Henrietta Lacks 3 December 2009 Colin Dayan ‘Dangerous’ Dogs 5 November 2009 Thomas Jones Bio Insecurity 18 December 2008 Caleb Crain Buckminster Fuller’s Visions 10 April 2008 Peter Campbell Engineers and Architects RELATED CATEGORIES Science, technology and mathematics Mathematics Americas North America ... print The Strange Case of Louis de Branges Karl Sabbagh Two years ago I wrote a book about the Riemann Hypothesis (for an account of the hypothesis see A.W. Moore’s article in this issue ). The proof of it is something that every mathematician would love to discover or – very much second best – see someone discover. One of the people I interviewed was Louis de Branges, a Franco-American mathematician at Purdue University in Lafayette, Indiana, with one significant proof already under his belt. De Branges was convinced that a mathematical field in which he was the acknowledged specialist would lead to a proof of the hypothesis. I have stayed in touch with him, and earlier this year, he told me he was putting the finishing touches to a proof he has been working on for 25 years. On 28 April this proof was published on the internet for other mathematicians to see and criticise: www.math.purdue.edu/~branges

78. Riemann Hypothesis Riemann Hypothesis Number Theory discussion Vote for Physics Forums in the physics.org Best Q A site category! (you have to register) Vote here http://www.physicsforums.com/showthread.php?t=78799

79. Constructing Nonresidues In Finite Fields And The Extended Riemann File Format Adobe PostScript View as HTML http://www.shoup.net/papers/nonresidues.ps

80. Id:A002410 - OEIS Search Results E. Bombieri, The Riemann Hypothesis in The Millennium Prize Problems Chap. 7 pp. 107128 Eds J. Carlson, A. Jaffe A. Wiles, Amer. Math. Soc. http://www.research.att.com/njas/sequences/A002410

Greetings from The On-Line Encyclopedia of Integer Sequences Hints Search: id:A002410 Displaying 1-1 of 1 results found. page 1 short internal text references ... off Nearest integer to imaginary part of n-th zero of Riemann zeta function. (Formerly M4924 N2113) list graph listen OFFSET COMMENT Contribution from Daniel Forgues (squid(AT)zensearch.com), Jul 24 2009: (Start) All nontrivial zeros on the critical line, of the form 1/2 + i*t, have an associated conjugate nontrivial zero of the form 1/2 - i*t. REFERENCES P. Borwein et al., The Riemann Hypothesis, Can. Math. Soc. (CMS) Ottawa ON 2007. J. Derbyshire, Prime Obsession, Penguin Books 2004. K. Devlin, The Millennium Problems, Chapter 1 (pp 19-62) Basic Books NY 2002. M. du Sautoy, The Music of the Primes, Fourth Estate/HarperCollins NY 2003. H. M. Edwards, Riemann's Zeta Function, Academic Press, NY, 1974, p. 96. J. P. Gram, Note sur les zeros de la fonction zeta(s) de Riemann, Acta Mathematica, 27 (1903), 289-304. C. B. Haselgrove and J. C. P. Miller, Tables of the Riemann Zeta Function. Royal Society Mathematical Tables, Vol. 6, Cambridge Univ. Press, 1960, p. 58.

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