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Riemann Hypothesis:     more books (41)

The Riemann hypothesis and Hilbert's tenth problem (Mathematics and its applications series;vol.4) by Sarvadamen Chowla, 1965 Residue: Repeating Decimal, Integer Factorization, Trial Division, Fundamental Theorem of Arithmetic, Riemann Hypothesis, Local Zeta-Function, Millennium Prize Problems Repunit: Integer Factorization, Trial Division, Fundamental Theorem of Arithmetic, Riemann Hypothesis, Local Zeta-Function, Clay Mathematics Institute, Millennium Prize Problems The Riemann hypothesis in algebraic function fields over a finite constants field by Helmut Hasse, 1968 Riemann Hypothesis: Bernhard Riemann, Riemann Zeta Function, Conjecture, Hilbert? Palya Conjecture, Generalized Riemann Hypothesis, Lee?Yang Theorem, Local Zeta-Function, Explicit Formula Prime Number: Natural Number, Divisor, Prime Number Theorem, Primality Test, Largest Known Prime Number, Mersenne Prime, Formula for Primes, Prime-Counting ... Theorem, Prime Gap, Riemann Hypothesis Stalking The Riemann Hypothesis: The Quest To Find The Hidden Law Of Prime Numbe by Daniel N Rockmore, 2005-01-01 Value-Distribution of L-Functions (Lecture Notes in Mathematics) by Jörn Steuding, 2007-07-20 Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings (Springer Monographs in Mathematics) by Michel L. Lapidus, Machiel van Frankenhuijsen, 2006-08-10 On the hypotheses which lie at the bases of geometry (Nature, a weekly illustrated journal of science) by Bernhard Riemann, 1873 Science and the Infinite or Through a Window in the Blank Wall by - Sydney T. Klein, 2009-07-18

lists with details

41. RIEMANN HYPOTHESIS
    riemann hypothesis. zeta(s) = 0 = Re(s) = 1/2. Proof zeta(s) = 0. = SUM(n=1 to99999…) n**s. = SUM(n=1 to 99999…) n**-sn**(2s-1) 0 =Re(s) 1 = 2Re(s)-1 1.  
    http://www.bearnol.pwp.blueyonder.co.uk/Math/riemann.htm

42. The Riemann Hypothesis
    Approaching the riemann hypothesis with Mathematica. The article ispublished in Comput. Math. Appl. , 37(1999), 8794. Abstract  
    http://www.cs.cmu.edu/~adamchik/articles/riemann.htm
    
    Extractions: The method of the analytic continuation of the function given on a part of the boundary into the whole domain is applied to the Riemann hypothesis on the Zeta function zeros. Comprehensive numerical experiments have been performed with the Mathematica V3.0.The computational approach confirmed the Riemann hypothesis.

43. 17a
    The Generalized riemann hypothesis. The Generalized riemann hypothesis(GRH)is the assertion that the riemann hypothesis is true, and  
    http://aimath.org/WWN/rh/articles/html/17a/
    
    Extractions: The Generalized Riemann Hypothesis The Generalized Riemann Hypothesis(GRH) is the assertion that the Riemann Hypothesis is true, and in addition the nontrivial zeros of all Dirichlet $L$-functions lie on the critical line Equivalently, GRH asserts that the nontrivial zeros of all degree 1 -functions lie on the critical line. The Modified Generalized Riemann Hypothesis(MGRH) is the assertion that the Riemann Hypothesis is true, and in addition the nontrivial zeros of all Dirichlet $L$-functions lie either on the critical line or on the real axis.

44. 16a
    The riemann hypothesis. The riemann hypothesis is the assertion that the nontrivialzeros of the Riemann zetafunction lie on the critical line .  
    http://aimath.org/WWN/rh/articles/html/16a/

45. The Riemann Hypothesis For The Goss Zeta Function For F_q[T], By Jeffrey T. Shea
    The riemann hypothesis for the Goss zeta function for F_qT, by JeffreyT. Sheats. Let q be a power of a prime p. We prove an assertion  
    http://www.math.uiuc.edu/Algebraic-Number-Theory/0096/
    
    Extractions: Let q be a power of a prime p. We prove an assertion of Carlitz which takes q as parameter. Diaz-Vargas' proof of the Riemann Hypothesis for the Goss zeta function for F_p[T] depends on his verification of Carlitz's assertion for the specific case q = p. Our proof of the general case allows us to extend Diaz-Vargas' proof to F_q[T].

46. The Impact Of The Infinite Primes On The Riemann Hypothesis For Characteristic P
    The impact of the infinite primes on the riemann hypothesis for characteristicp Lseries, by David Goss. In \cite{go2} we proposed  
    http://www.math.uiuc.edu/Algebraic-Number-Theory/0299/

47. The Prime Glossary: Riemann Hypothesis
    This pages contains the entry titled 'riemann hypothesis.' Come explore a new primeterm today! riemann hypothesis (another Prime Pages' Glossary entries).  
    http://primes.utm.edu/glossary/page.php?next=residue

48. The Prime Page's Links++: Theory/conjectures/Riemann
    Add Update New Popular . The riemann hypothesis is perhapsthe most central and important of all prime number conjectures.  
    http://primes.utm.edu/links/theory/conjectures/Riemann/
    
    Extractions: (Added: 20-Aug-2000 Hits: 421 Rating: 5.50 Votes: 2) Rate It The Riemann Hypothesis: Spectral Interpretation - If the zeros can be interpreted as the eigenvalues of 1/2+iT, where T is a Hermitian operator on some Hilbert space, then since the zeros of a Hermitian operator are real, the Riemann hypothesis follows.

49. Polynomial Families Satisfying A Riemann Hypothesis
    Congressus Numerantium (in review). Ömer Egecioglu and Charles Ryavec.Polynomial Families Satisfying a riemann hypothesis. Abstract.  
    http://www.cs.ucsb.edu/~omer/personal/abstracts/riemann.html

50. The Riemann Hypothesis
    Millennium Prize Math Problems. The riemann hypothesis. The riemann hypothesisasserts that all interesting solutions of the equation. z(s) = 0.  
    http://antigravitypower.tripod.com/MathProblems/riemann.html
    
    Extractions: Back to Millennium Math Prize Index Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function “ z (s)” called the Riemann Zeta function . The Riemann hypothesis asserts that all interesting solutions of the equation z (s) = lie on a straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers. Mathematical Description authored by Enrico Bombieri (PDF files are viewed with Adobe's Acrobat Reader

51. A Complete Vinogradov 3-primes Theorem Under The Riemann Hypothesis
    A complete Vinogradov 3primes theorem under the riemann hypothesis.JM Deshouillers, G. Effinger, H. te Riele and D. Zinoviev. Abstract.  
    http://www.mpim-bonn.mpg.de/external-documentation/era-mirror/1997-01-015/1997-0

52. Riemann Hypothesis And Computer Science
    Prof. Rusins Freivalds. Department of Computer Science, University of Latvia,Riga. riemann hypothesis and Computer Science. Eine Gemeinschaftsveranstaltung  
    http://www.uni-greifswald.de/~wwwmathe/inf/gi/20.10.97.html
    
    Extractions: 17 489 Greifswald gez. Prof. Dr. L. Voelkel Riemann Hypothesis on the nontrivial zeros of the zeta-function was a by-product in B.Riemann's attempt to solve a problem in number theory. Since Riemann's paper of 1859 the attitude of mathematicians to this area has changed very much. The problem attempted by B.Riemann was solved in 1896 by J.S.Hadamard and Ch.J. de la Vallee-Poussin (the prime number theorem). However the by-product has turned into one of the most famous unsolved problems in mathematics. It has turned out to be equivalent to unsolved problems in many areas of mathematics. We study space complexity for the weak recognition of languages. If L(n) is a small function, there can be languages A such that A is weakly recognized in deterministic space L(n) but the complement language of A is not. The language PERFECT_SQUARES needs deterministic space

53. AMCA: A Riemann Hypothesis And Simplicity Conjecture For Characteristic $p$ $L$-
    A riemann hypothesis and simplicity conjecture for characteristic $p$ $L$seriesby David Goss The Ohio State University and Journal of Number Theory  
    http://at.yorku.ca/cgi-bin/amca/cadx-49

54. AMCA: Nyman's Criterion For The Riemann Hypothesis Presented By Michel Balazard
    Nyman's criterion for the riemann hypothesis by Michel Balazard CNRS,University Bordeaux 1, FRANCE In his 1950 PhD thesis, Bertil  
    http://at.yorku.ca/cgi-bin/amca/caew-10
    
    Extractions: CNRS, University Bordeaux 1, FRANCE In his 1950 PhD thesis, Bertil Nyman proved that the Riemann hypothesis is equivalent to the density in L (0,1) of a certain subspace. I will discuss some results and open questions connected with this criterion. Date received: March 15, 2000 Atlas Mathematical Conference Abstracts

55. The Riemann Hypothesis
    The riemann hypothesis. The function. The famous riemann hypothesis is equivalentto the assertion that. (This is another $1000000 prize problem.).  
    http://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture4/html/node5.htm
    
    Extractions: Next: About this document ... Up: How many primes are Previous: Counting Primes Today The function is also a good approximation to The famous Riemann Hypothesis is equivalent to the assertion that (This is another $1000000 prize problem.) pi(10^22) = 201467286689315906290 Li(10^22) = 201467286691248261498.1505... (using Maple) Log(x)/(x-1) = 201381995844659893517.7648... (pari)

56. The Riemann Hypothesis
    The riemann hypothesis. millennium prize problems / the riemann hypothesis problem. Theriemann hypothesis asserts that all interesting solutions of the equation.  
    http://www.mi.sanu.ac.yu/~zorano/izazovi21vek/riemann.html
    
    Extractions: Clay Mathematics Institute millennium prize problems / the riemann hypothesis problem Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function “ z (s)” called the Riemann Zeta function . The Riemann hypothesis asserts that all interesting solutions of the equation z (s) = lie on a straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers. Mathematical Description authored by Enrico Bombieri

57. Mathematica Information Center: Approaching The Riemann Hypothesis With Mathemat
    Title, Approaching the riemann hypothesis with Mathematica, Authors, Lev Aizenberg. Theresults of the experiments support the riemann hypothesis. Subject,  
    http://library.wolfram.com/database/Articles/1398/

58. Mathematica Information Center: The Riemann Hypothesis
    Courseware, Demos, MathSource, Technical Notes, Title, Downloads, The RiemannHypothesis, Authors, Lev Aizenberg. Organization BarIlan University, Israel.  
    http://library.wolfram.com/database/Demos/126/

59. Riemann Hypothesis
    The summary for this Korean page contains characters that cannot be correctly displayed in this language/character set.  
    http://www.postech.ac.kr/math/study/read/read027-Riemann_Hypothesis.html
    
    Extractions: Çؼ®Àû ¼ö·Ð¿¡¼­´Â °ü·ÊÀûÀ¸·Î º¹¼Ò¼ö¸¦ s·Î Ç¥½Çϸç, ±×°ÍÀÇ ½Ç¼ö ºÎºÐÀº ¥ò, Çã¼öºÎºÐÀ» t·Î Ç¥½ÇÑ´Ù. Áï, s = ¥ò + itÀÌ´Ù. ¸®¸¸ Á¦Å¸ ÇÔ¼ö´Â ¾Æ·¡¿Í °°ÀÌ ±Þ¼ö·Î Ç¥ÇöµÇ´Â º¹¼Ò¼ö ÇÔ¼öÀÌ´Ù. ¥æ(s) = p ÀÓÀ» º¸¿´´Âµ¥ ÀÌ°ÍÀº ¼Ò¼öÀÇ °³¼ö´Â ¹«ÇÑÇÏ´Ù´Â À¯Å¬¸®µå(Euclid) Á¤¸®ÀÇ »õ·Î¿î Áõ¸íÀÌ´Ù. ¿ÀÀÏ·¯ÀÇ ÀÛ¾÷ÀÇ Áß¿äÇÑ Àǹ̴ Á¦Å¸ ÇÔ¼ö°¡ ¼Ò¼öÀÇ ºÐÆ÷¿Í °ü·µÇ¾î ÀÖ´Ù´Â »ç½ÇÀÇ ¹ß°ßÀ̸ç, ÀÌ°ÍÀº Çؼ®ÇÐÀû ¼ö·ÐÀÇ ±â¿øÀ̶ó°í ¸»ÇÒ ¼ö ÀÖ´Ù. ¥æ(s) = x s + 1 dx ¿©±â¼­ ¸®¸¸ ³í¹®ÀÇ ÁÖ¿ä ³»¿ëÀ» °£´ÜÈ÷ ¾ð±ÞÇÒ ÇÊ¿ä°¡ ÀÖ´Ù. ¸®¸¸Àº Á¦Å¸ ÇÔ¼öÀÇ Á¤ÀÇ¿ªÀ» º¹¼Ò¼ö Æò¸é Àü¼·Î È®ÀåÇÑ´Ù. À§ Àý¿¡¼­ ¼­¼úÇÑ ¹æ¹ý°ú´Â ´Þ¸®, ±×´Â °¨¸¶ ÇÔ¼ö(gamma function)ÀÇ ÀûºÐÇ¥ÇöÀ» ÀÌ¿ëÇÑ´Ù. ¸®¸¸Àº À¯¸íÇÑ ÇÔ¼ö ¹æÁ¤½Ä(functional equation)À» À¯µµÇÑ´Ù. ) ¥æ(1 - s) ÀÌ ¹æÁ¤½ÄÀº Á¦Å¸ÇÔ¼ö°¡ Á÷¼± ¥ò = 1/2¿¡ ´ëÇÏ¿© ¸ðÁ¾ÀÇ ´ëĪ¼ºÀ» °®°í ÀÖÀ½À» ½»çÇÑ´Ù. ƯÈ÷ ÀÚ¸íÇÏÁö ¾ÊÀº ¿µÁ¡µéÀº Á÷¼± ¥ò = 1/2¿¡ ´ëÇÏ¿© ´ëĪÀûÀ¸·Î À§Ä¡ÇØ¾ß ÇÔÀ» ¾Ë ¼ö ÀÖ°í, ÀÌ°ÍÀº ¸®¸¸ °¡¼³ÀÇ ³í°Å Áß¿¡ ÇϳªÀÌ´Ù. »ç½Ç»ó, ¸®¸¸°¡¼³ÀÌ ÂüÀ̶ó°í ¸»ÇÒ ¼ö ÀÖ´Â ÀÌ·ÐÀû ÀÌÀ¯´Â, ÀÌ ÇÔ¼ö ¹æÁ¤½Ä¹Û¿¡ ¾ø´Ù°í Çصµ °ú¾ðÀÌ ¾Æ´Ï´Ù. s = 1/2 + it¸¦ À§ ½ÄÀÇ Áº¯¿¡ ´ëÀÔÇÏ¿© ¾ò¾îÁö´Â ÇÔ¼ö¸¦ ¥î(t)¶ó ³õ´Â´Ù. ¥î´Â ÀüÇؼ® ÇÔ¼öÀÌ°í, ¥îÀÇ ¿µÁ¡µéÀº ¸ðµÎ Çã¼ö ºÎºÐÀÌ -i/2¿Í i/2 »çÀÌÀÇ ¿µ¿ª ¾È¿¡ ÀÖ°í, ¸®¸¸ °¡¼³Àº ¥îÀÇ ¿µÁ¡ÀÌ ¸ðµÎ ½Ç¼ö¶ó´Â °Í°ú °°´Ù.

60. Riemann Hypothesis Information Sites
    Reviewed riemann hypothesis sites, by people who know riemann hypothesisand work with riemann hypothesis. NUMBERSorg.com. Search  
    http://numbersorg.com/NumberTheory/Analytic/RiemannHypothesis/
    
    Extractions: See Also: Science: Math: Number Theory: Open Problems Easy Proof of Riemann's Hypothesis - Generalisations of the zeta function might provide a proof of Riemann's hypothesis. The Music of the Primes - A popular article by Marcus du Sautoy on the Riemann Hypothesis; Science Spectra, Issue 11. Papers on Zeros of the Riemann Zeta Function - By Andrew Odlyzko. Poem about the Riemann Zeta Function - A mathematical hyper-poem. Proof of Riemann's Hypothesis - A claimed proof of Riemann's Hypothesis. The Riemann Hypothesis - Notes by Steven Finch. The Riemann Hypothesis - A prime pages article by Chris K. Caldwell. The Riemann Hypothesis - Papers and other links related to RH compiled by Dan Bump. Riemann's Hypothesis - A beginners guide by Jon Perry. Riemann Hypothesis - A short article by Krzysztof Maslanka with numerical examples and graphics. Riemann Hypothesis - Article with links to other resources from MathWorld.

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