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

RIEMANN HYPOTHESIS Proof: zeta(s) = = SUM(n=1 to 99999 ) n**-s = SUM(n=1 to 99999 ) n**(s-1) = zeta(1-s) i.e. Re(s) =1/2

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

Approaching the Riemann Hypothesis with Mathematica The article is published in Comput. Math. Appl. Abstract 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. Mathematica Notebook Please send corrections to Victor S. Adamchik Computer Science Department, Carnegie Mellon University, Pittsburgh, PA

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/

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. Back to the main index for The Riemann Hypothesis.

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/

The Riemann Hypothesis The Riemann Hypothesis is the assertion that the nontrivial zeros of the Riemann zeta-function lie on the critical line Back to the main index for The Riemann Hypothesis.

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/

The Riemann Hypothesis for the Goss zeta function for F_q[T], by Jeffrey T. Sheats 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]. rh.ps (405022 bytes) rh.ps.gz (118508 bytes) Jeffrey T. Sheats

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/

The impact of the infinite primes on the Riemann hypothesis for characteristic p L-series, by David Goss co.dvi (93456 bytes) [2001 Jun 8] co.dvi.gz (39221 bytes) co.ps.gz (118008 bytes) David Goss

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/

Links related to Prime Numbers Add Update New Popular The Riemann Hypothesis is perhaps the most central and important of all prime number conjectures. Top theory conjectures : Riemann Resources in theory : conjectures : Riemann Prime Glossary's entry: Riemann hypothesis (Added: 20-Aug-2000 Hits: 420 Rating: Votes: 0) Rate It Riemann hypothesis - A short introduction to this difficult conjecture. (Added: 20-Aug-2000 Hits: 663 Rating: 8.00 Votes: 1) Rate It Riemann Hypothesis from Eric Weisstein's World of Mathematics - Definition, mathematical theory, references, links... (Added: 20-Aug-2000 Hits: 281 Rating: Votes: 0) Rate It The Riemann Hypothesis - Includes elementary restatement of the Riemann hypothesis, Mills' constant, de Bruijn-Newman constant, and the Gaussian unitary ensemble hypothesis. (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. (Added: 20-Aug-2000 Hits: 306 Rating: 8.00 Votes: 1)

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

Congressus Numerantium (in review). Polynomial Families Satisfying a Riemann Hypothesis Abstract. omer@cs.ucsb.edu

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

Get Four DVDs for $.49 each. Join now. Tell me when this page is updated Back to Main AntiGravity Propulsion Introduction Page Back to Millennium Math Prize Index Millennium Prize Math Problems The Riemann Hypothesis 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 Back to Main AntiGravity Propulsion Introduction Page Back to Millennium Math Prize Index

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

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ A complete Vinogradov 3-primes theorem under the Riemann hypothesis J.-M. Deshouillers, G. Effinger, H. te Riele and D. Zinoviev Abstract. We outline a proof that if the Generalized Riemann Hypothesis holds, then every odd number above is a sum of three prime numbers. The proof involves an asymptotic theorem covering all but a finite number of cases, an intermediate lemma, and an extensive computation. Retrieve entire article TeX source DVI PostScript Article Info ERA Amer. Math. Soc. (1997), pp. 99-104 Publisher Identifier: S 1079-6762(97)00031-0 Mathematics Subject Classification . Primary 11P32 Key words and phrases . Goldbach, Vinogradov, 3-primes problem, Riemann hypothesis Received by the editors February 26, 1997 Posted on September 17, 1997 Communicated by Hugh Montgomery Comments (When Available) J.-M. Deshouillers Mathematiques Stochastiques, UMR 9936 CNRS-U.Bordeaux 1, U.Victor Segalen Bordeaux 2, F33076 Bordeaux Cedex, France E-mail address: dezou@u-bordeaux2.fr

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

Prof. Rusins Freivalds Department of Computer Science, University of Latvia, Riga Riemann Hypothesis and Computer Science Eine Gemeinschaftsveranstaltung des und der Regionalgruppe Vorpommern der Termin: Montag, 20. Oktober 1997 Uhrzeit: 12.30 Uhr Ort: Jahnstr. 15a 17 489 Greifswald gez. Prof. Dr. L. Voelkel Abstract 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

AMCA Document # cadx-49 Millennial Conference on Number Theory May 21-26, 2000 University of Illinois Urbana, IL, USA Organizers B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp View Abstracts Conference Homepage A Riemann hypothesis and simplicity conjecture for characteristic $p$ $L$-series by David Goss The Ohio State University and Journal of Number Theory Z , k with Q Date received: March 3, 2000 Atlas Mathematical Conference Abstracts

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

AMCA Document # caew-10 Millennial Conference on Number Theory May 21-26, 2000 University of Illinois Urbana, IL, USA Organizers B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp View Abstracts Conference Homepage Nyman's criterion for the Riemann hypothesis by Michel Balazard 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

Next: About this document ... Up: How many primes are Previous: Counting Primes Today The Riemann Hypothesis 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) William A Stein 2001-09-19

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

Clay Mathematics Institute The Riemann Hypothesis 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/

All Collections Articles Books Conference Proceedings Courseware Demos MathSource: Packages and Programs Technical Notes Title Approaching the Riemann Hypothesis with Mathematica Authors Lev Aizenberg Organization: Bar-Ilan University, Israel Victor Adamchik Organization: Carnegie-Mellon University Department: Computer Science Vadim E. Levit Organization: Tel-Aviv University, Israel Department: Department of Computer Systems Journal / Anthology The Mathematica Journal Year: Volume: Issue: Page range: Description The method of analytic continuation is used to formulate a condition that is equivalent to the Riemann hypothesis on the zeros of the zeta function. Numerical experiments to verify the condition are performed with Mathematica 3.0. The results of the experiments support the Riemann hypothesis. Subject Mathematics Calculus and Analysis Special Functions URL http://www.mathematica-journal.com/issue/v7i1/

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/

All Collections Articles Books Conference Proceedings Courseware Demos MathSource: Packages and Programs Technical Notes Title The Riemann Hypothesis Authors Lev Aizenberg Organization: Bar-Ilan University, Israel Victor Adamchik Organization: Carnegie-Mellon University Department: Computer Science Vadim E. Levit Organization: Tel-Aviv University, Israel Department: Department of Computer Systems Subjects Mathematics Calculus and Analysis Complex Analysis Mathematics ... Number Theory Keywords Riemann zeta function, analytic continuation Downloads Riemann.nb (185.9 KB) - Mathematica Notebook

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

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) = n = 1 n s Á¦Å¸ ÇÔ¼ö¿¡ ´ëÇÑ ¿¬±¸´Â ¿ÀÀÏ·¯(Eular)±îÁö °Å½½·¯ ¿¶ó°£´Ù. ±×´Â Á¦Å¸ ÇÔ¼ö°¡ ´ÙÀ½°ú °°Àº °ö¼À°ø½Ä(product formula)À» ¸¸Á·ÇÔÀ» °üÂûÇÏ¿´´Ù. ¥æ(s) = p p s ¿©±â¼­ °öÀº ¸ðµç ¼Ò¼ö p¿¡ °üÇÑ °ÍÀÌ´Ù. ±×´Â ¶ÇÇÑ p 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) = 1 - s n = 1 n - 1 n s ¥æ(s) = s s - 1 - 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. s(s - 1)¥ð -s/2 s ) ¥æ(s) = s(s - 1)¥ð -(1 - s)/2 1 - s ) ¥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/

NUMBERSorg.com Search SPYorg.com (Not sure of spelling? Use first letters and * such as abc* or abcd* or abcde*) Match:.. All Any Format: Long Short Search Words: Top Science Math Number Theory ... Analytic : Riemann Hypothesis 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.

Page 3     41-60 of 85    Back | 1  | 2  | 3  | 4  | 5  | Next 20