61. MathUniverse Entry - 3 July 2002: Riemann Hypothesis Conference Previous entry Let there be light Main Index Next entry MarkovModels and Money 3 July 2002. media riemann hypothesis Conference. http://mathuniverse.com/archives/00000002.htm

Previous entry: "Let there be light..." Main Index Next entry: "Markov Models and Money" 3 July 2002 media : Riemann Hypothesis Conference Bruce Schechter, in his article 143-Year-Old Problem Still Has Mathematicians Guessing reports on a conference at the Courant Institute on the Riemann Hypothesis. The article is actually more on the history of the problem and also gives one a little idea what the Riemann Hypothesis is about. Mr. Schechter does a rather good job with the subject, managing to indicate the main thrust of the hypothesis, which happens to link number theory and complex analysis in a beautiful alliance. If you are the type that can handle heavy-duty math, then check out MathWorld's item on the Riemann Hypothesis (Warning: this takes a graduate level understanding of complex analysis to decrypt. And even then, don't be surprised if you can't read anything that dense.) I find it interesting that some of the greatest theorems or conjectures in mathematics link "pure" and "applied" math. I do realize that many outside of mathematics have the idea that applied math is what engineers do, and pure math involves proofs, lots of variables, and sometimes nary an actual numeral in sight. Amongst mathematicians, particular fields are considered are applied: discrete math (the math computer science people do), probability, analysis, differential geometry, and that's all I can think of off the top of my head. But a great many of these "applied" people are working within the framework of of definition, theorem, proof; and how pure can "pure" math be, if number theory is being used to create and crack important cryptographic systems?

62. The Riemann Hypothesis The riemann hypothesis (the zeros of the zeta function have real part 1/2). Summary In1901 von Koch showed that the riemann hypothesis is equivalent to http://www.tamu-commerce.edu/coas/math/FACULTY/GRADS/denney/proofs/riemann.htm

Courtesy of Chris K. Caldwell of University of Tennessee at Martin The Riemann Hypothesis (the zeros of the zeta function have real part 1/2) Summary: When studying the distribution of prime numbers Riemann extended Euler's zeta function (defined just for s with real part greater than one) to the entire complex plane ( sans simple pole at s = 1). Riemann noted that his zeta function had trivial zeros at -2, -4, -6, ... and that all nontrivial zeros were symmetric about the line Re( s The Riemann hypothesis is that all nontrivial zeros are on this line. In 1901 von Koch showed that the Riemann hypothesis is equivalent to: The Riemann Hypothesis: Euler studied the sum for integers s (1) is infinite). Euler discovered a formula relating k ) to the Bernoulli numbers yielding results such as and . But what has this got to do with the primes? The answer is in the following product taken over the primes p (also discovered by Euler): Euler wrote this as Riemann later extended the definition of s ) to all complex numbers s (except the simple pole at s =1 with residue one). Euler’s product still holds if the real part of

63. Solid Model Of Zeta Function Constructed For Studying The Riemann Hypothesis Larry Carter Solid Model of Zeta Function Constructed for Studyingthe riemann hypothesis. SDSC senior fellow and UCSD computer http://www.sdsc.edu/SDSCwire/v1.7/2017.Carter.html

Larry Carter: Solid Model of Zeta Function Constructed for Studying the Riemann Hypothesis SDSC senior fellow and UCSD computer scientist Larry Carter applied rapid prototyping technology to study the zeta function and the Riemann hypothesis. The Riemann hypothesis has been called the most important unsolved problem of mathematics. The Riemann zeta function is defined for all complex numbers z as: zeta( z) = The zeta function plays an intricate role in number theory. For instance, the zeros of zeta are intimately connected to variations in the distribution of prime numbers. The Riemann hypothesis states that whenever zeta( z ) = 0, then z must be on the critical line iy , where i is the square root of -1 This hypothesis is related to the difficulty of testing whether a number is a primein fact, there is an algorithm that is known to be fast only under the assumption that a certain generalization of the Riemann hypothesis is true. Years ago, determining whether a number is prime was mainly a pastime for mathematicians; however, today, very large prime numbers (with 50 or 100 digits) are necessary ingredients for certain public-key cryptography systems. Carter and SDSC scientific visualization researcher Mike Bailey constructed a three-dimensional model of the zeta function with SDSC's Laminated Object Machine (LOM)a machine that uses rapid prototyping (RP) technology to construct solid models from geometric data. The model plots the absolute value of zeta(

64. Random Matrix Theory( Riemann Hypothesis) Random Matrix Theory( riemann hypothesis). Follow Ups Post Followup Relativity XV FAQ Posted by sol on January 28, 2003 at 205005 http://superstringtheory.com/forum/relboard/messages15/185.html

String Theory Discussion Forum String Theory Home Forum Index Random Matrix Theory( Riemann Hypothesis) Follow Ups Post Followup Relativity XV FAQ Posted by sol on January 28, 2003 at 20:50:05: In Reply to: Re: The big bang, and its topology posted by Haelfix on January 28, 2003 at 07:42:23: Haelfix, Just a couple of questions here. If no metric is defined for a system, then we are in a branch of mathematics known as topology, which deals with how regions of space are connected to one another. The Story of Mathematics , by Richard Mankiewicz,Pg 131 What strings seeks to illustrate, has been a troubling issue in terms of what Berhard Riemann had to offer in terms of his Hypothesis? Now what do we find that brings value to what is inherent in the identification of what the KK tower( Kaluza Klein Tower) brings to understanding in terms of those energies, and what we find is a move beyond the four dimensional aspect of spacetime, and to interpretations here, on those Eigen state determination of the Quantum systems? I draw your attention back to a brief discussion on the 5th Solvay meetings and the congregation of the post I have written here in links.

65. Riemann Hypothesis Re: Friendly AI riemann hypothesis Re Friendly AI. rbfar@ebuilt.com wrote What's the ReimannHypothesis BTW, my bad for mispelling Riemann in the original subject line. http://www.xent.com/pipermail/fork/2001-May/000233.html

Riemann Hypothesis Re: Friendly AI Jeff Bone jbone@jump.net Sun, 27 May 2001 02:17:59 -0500 Previous message: Reimann Hypothesis Re: Friendly AI Next message: Reimann Hypothesis Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... rbfar@ebuilt.com What's the Reimann Hypothesis http://www.claymath.org/prizeproblems/riemann.htm http://www.claymath.org/prizeproblems/riemann.pdf Previous message: Reimann Hypothesis Re: Friendly AI Next message: Reimann Hypothesis Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

66. Citation ACM symposium on Theory of computing toc 1985 , Providence, Rhode Island, UnitedStates riemann hypothesis and finding roots over finite fields Author MD A http://portal.acm.org/citation.cfm?id=22159&dl=ACM&coll=portal&CFID=11111111&CFT

67. Archimedes Plutonium Two proofs riemann hypothesis. by Archimedes Plutonium this is a return Thereforethe riemann hypothesis is proved. QED My second proof http://www.newphys.se/elektromagnum/physics/LudwigPlutonium/File125.html

Two proofs Riemann Hypothesis by Archimedes Plutonium this is a return to website location http://www.newphys.se/elektromagnum/physics/LudwigPlutonium/

68. The Generalized Riemann Hypothesis And The Birch And Swinnerton x TO 1/x MOD p. Does the map sending x to 1/x mod p behave like arandom signed involution? Let L(p) be the length of the largest. http://www.math.nyu.edu/Courses/V63.0393/projects/modp/modp.htm

x TO 1/x MOD p Does the map sending x to 1/x mod p behave like a random signed involution? Let L(p) be the length of the largest Jon Bober investigated the distribution of L(p) (appropriately rescaled), and compared the results to the Tracy-Widom distributions; it is known that if one considers all permutations, as well as some subsets, the distribution of the longest increasing subsequence is given by the Tracy-Widom distributions. This research was inspired by a problem posed by Jim Propp. PAPER: inversemod.ps inversemod.pdf inversemod.dvi inversemod.latex FIGURES: meannew3.ps normalized.ps stdev3.ps tw.ps ... unnormal.ps CODE: ntlsubseq.cpp readdata.cpp HANDOUTS: Handout on Randomness of x to 1/x mod p

69. The Generalized Riemann Hypothesis And The Birch And Swinnerton GERMAIN PRIMES. A Germain prime is a prime p such that p and 2p+1 areprime. HardyLittlewood conjectured the number of Germain. primes http://www.math.nyu.edu/Courses/V63.0393/projects/germainprimes/germain.htm

GERMAIN PRIMES A Germain prime is a prime p such that p and 2p+1 are prime. Hardy-Littlewood conjectured the number of Germain as comparing the distribution of spacings between Germain primes to a Poisson process. PAPERS: germain.dvi germain.pdf germain.ps germain.tex ... refs.bib.txt FIGURES: 1.ps 2.ps 3.ps 4.ps ... conv.ps PROGRAM: germain.c HANDOUTS: Poissonian Behavior Circle Method

70. Ask Jeeves: Search Results For "Riemann Hypothesis" Popular Web Sites for riemann hypothesis . Search Results 1 10Ranked by Popularity, Next . 1. The riemann hypothesis Spectral http://webster.directhit.com/webster/search.aspx?qry=Riemann Hypothesis

71. StudyWorks! Online : Eight Million Dollar Problems On the other hand, the riemann hypothesis (one of the Clay Instituteproblems) has been around only since 1859. Many people have http://www.studyworksonline.com/cda/content/article/0,,NAV4-44_SAR193,00.shtml

StudyWorks News Science News Environmental News Math News ... Earth Observatory Eight Million Dollar Problems The new Clay Mathematics Institute has made a stunning offer: if you solve seven difficult mathematics problems, you will receive seven million dollars. As with any offer that sounds too good to be true, there is a catch. The seven problems chosen by the Institute are suspected to be among the most intractable of all unsolved mysteries ever conceived by the human mind. Add to the jackpot an offer by two publishers, Bloomsbury (in America) and Faber and Faber (in Great Britian). They have announced a one million dollar prize for the first person to prove Goldbach's Conjecture by March, 2002. Your best chance for collecting some cash would be to focus on just one problem, rather than all eight. The odds of any one person solving two such problems are vanishingly small. You would then be eligible for just one million dollars, of course. You would also be wise to forget about trying to prove Goldbach's Conjecture: the two-year time limit makes this infeasible, especially considering that the problem has baffled mathematicians since 1742! On the other hand, the Riemann Hypothesis (one of the Clay Institute problems) has been around only since 1859. Many people have devoted their lives to trying to prove this, but all have failed. There are many ways of stating the Riemann Hypothesis. Some are profound and complex; others are elementary and seemingly silly. Here is an example of the latter.

72. Leuschke.org Archives :: February 10, 2002 - February 16, 2002 The riemann hypothesis. To answer Juliet's first question, though, Yes, the RiemannHypothesis is perhaps the greatest remaining unsolved problem in pure math. http://www.leuschke.org/log/archives/week_2002_02_10.html

@import "http://www.leuschke.org/log/logstyle.css"; log home Saturday 16 Feb 02 P2P review I signed up for Peer-to-Peer Weblog Review . I don't generally get excited about these memes (Blogger Insider, for instance, leaves me cold), but this might be fun. Go check it out. comments [0] link Image enhancer I've been looking for something like this: a free digital camera enhancer . DCE automagically reduces noise, adjusts balance, and smooths images. Find the right settings for your camera and let it do its thing. Very cool. comments [0] link Friday 15 Feb 02 Beauty and Elegance in mathematics Beauty is truth, truth beauty, that is all Ye know on earth, and all ye need to know. Let's talk about Juliet's second question : "just how important are the concepts of "beauty" and "elegance" in mathematics?" Let's kick it off with a few more quotations My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful. Hermann Weyl, (1885 - 1955) The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance. J.J. Sylvester Presidential Address to British Association, 1869.

73. Riemann Hypothesis - Acapedia - Free Knowledge, For All Friends of Acapedia riemann hypothesis. From Wikipedia, the free encyclopedia. Mostmathematicians believe the riemann hypothesis to be true. http://acapedia.org/aca/Riemann_hypothesis

var srl33t_id = '4200';

74. Telecom.html Fujii, A. ``A remark on the riemann hypothesis. Comment. Math. Univ. St. A remarkon the riemann hypothesis. Proc. Japan Acad., Ser. A 57 (1981), 326330 . http://www.math.jussieu.fr/~miw/telecom/biblio-Amoroso.html

par Francesco AMOROSO Amoroso, F. ``On the heights of a product of cyclotomic polynomials." Number theory, I (Rome, 1995). Rend. Sem. Mat. Univ. Politec. Torino (1995), no. 3, 183191. Amoroso, F. ``Algebraic numbers close to 1 and variants of Mahler's measure." J. Number Theory (1996), no. 1, 8096. ``Some properties of the local discrepancy of Farey sequences." Atti Accad. Sci. Istit. Bologna Cl. Sci. Fis. Rend (13) (1980/81), no. 1-2, 163-173. ``On the uniform distribution (mod 1) of the Farey fractions and l^p spaces." Math. Ann. (1988), no. 3, 413-422. Franel, J. Fujii, A. ``A remark on the Riemann hypothesis." Comment. Math. Univ. St. Pauli Fujii, A. ``Some explicit formulae in the theory of numbers. A remark on the Riemann Hypothesis." Proc. Japan Acad., Ser. A Huxley, M.N. ``The distribution of Farey points, I." Acta Arith. Kanemitsu, S. and Yoshimoto, M. ``Farey series and the Riemann hypothesis." Acta Arith. (1996), no. 4, 351-374. Kanemitsu, S. and Yoshimoto, M. ``Farey series and the Riemann hypothesis. III." Ramanujan J.

75. VERGLAS.ORG RIEMANN HYPOTHESIS The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.verglas.org/blackIce/riemann.html

<®Ó2IíR Kw¹¶²Œm,–e@‹T"Ø8Ùÿܕâƒ. tüLÑ.ÆT‡ŒAmðñz¼ç¸†™LQèJ÷*Ò ‹°gh‘Œ]l=:ãþØIM¿S0Áz×àA²(ýõÀ âM' <®Ó2IíR×õj¿G,Z ` êbe EèP­¼å¥0ݘ <•âT8‰í]MÌÞqôïÁގ¹¡é-géÒZž²8N!’»‚gйnÚ7®Ö»åúp/ÛFBA™aB_ŸÅ§–òs÷ÿÑóŠ4 <¦lŒñŽ?ë:I˜ <@[zÁ:r§ÓG˜•N붱ß팔•ÚG <i»0t­Ð# ²KDÏI®¾N´µû·l½,t‰¤±lS¤ < l$Äc§E€‰â‘¾¾òµ¬'a'- ¯PYb”–ÎÍSÄú«žáíÞ+q,ì.¦–D»D' “‘ m9‚µÅhZ„`»-ó-˜cC ÜîQôí­È íÏíú€Õ/ng ;Ú¶Œy3’Ÿ™œ.ï‚`¡÷ @øù kęÕk¸ ûk$=cÐS»H¹³¢@®Ì·mïƒtþ1^Øp¤dñ; ‡ö.Qö 'DÎ¥ëS¦þišØ ~µ÷fr žMoðŠª»ÜT3D–7÷ÀZÍ:̀×Õq³2> kXÿ–¦A±27~±ÜÜ <´Œ¬› Mƒˆ i hope the fbi leaves me alone for this!!! backtracking:: main city math

76. Citations: Riemann Hypothesis And Finding Roots Over Finite Fields - Huang (Rese MingDeh A. Huang. riemann hypothesis and finding roots over finite fields. Ming-DehA. Huang. riemann hypothesis and finding roots over finite fields. http://citeseer.nj.nec.com/context/774338/0

Ming-Deh A. Huang. Riemann hypothesis and finding roots over finite fields . In Proceedings of the 17th Annual Symposium on Theory of Computing, pages 121130, New York, 1985. Association for Computing Machinery. Home/Search Document Not in Database Summary Related Articles This paper is cited in the following contexts: Open Problems in Number Theoretic Complexity, II - Adleman, McCurley (4 citations) (Correct) ....It is also known that the least quadratic nonresidue is almost always small [Erd61] so C12 can be solved in deterministic polynomial time for almost all inputs. Rem 12 94 On the problem of calculating kth power non residues in GF(p n ) the following is known. On ERH, the algorithm of Huang , generalized by Evdokimov [Evd89] constructs a kth power nonresidue, in GF(p n ) in deterministic time (kn log p) O(1) Buchmann and Shoup [BS91] on ERH, construct a kth power non residue in GF(p n ) in deterministic time (log p) O(n) Bach [Bac90] on ERH, has given explicit bounds . ....oversight that we did not mention the work of Schoof [Sch85] on this problem in our earlier manuscript. Schoof proved that for fixed a, there exists a deterministic algorithm with running time polynomial in log p.

77. [quant-ph/9707036] Lorentz-Invariant Hamiltonian And Riemann Hypothesis LorentzInvariant Hamiltonian and riemann hypothesis. Author Susumu OkuboComments 13 pages, TEX Report-no UR-1502 Journal-ref J.Phys. http://arxiv.org/abs/quant-ph/9707036

Quantum Physics, abstract quant-ph/9707036 Lorentz-Invariant Hamiltonian and Riemann Hypothesis Author: Susumu Okubo Comments: 13 pages, TEX Report-no: UR-1502 Journal-ref: J.Phys. A31 (1998) 1049-1057 We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to infinite-dimensional representation of the Lorentz group have many interesting properties. Especially, a relationship exists between the zero zeta function condition and the absence of trivial representations in the wave function. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Links to: arXiv quant-ph find abs

78. The Riemann Hypothesis The riemann hypothesis. home / millennium prize problems / the riemann hypothesis. Theriemann hypothesis asserts that all interesting solutions of the equation. http://elib.zib.de/pub/Misc/MillenniumPrizeProblems/www.claymath.org/prize_probl

Clay Mathematics Institute [home] [index] Annual Meeting Researchers ... Other The Riemann Hypothesis home millennium prize 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 [home] [index] webmaster@claymath.org

79. Time.9910: [time 942] Riemann Hypothesis In Sharpened Form time 942 riemann hypothesis in sharpened form. Matti Pitkanen (matpitka@pcu.helsinki.fi)Mon, 18 Oct 1999 104833 +0300 (EET DST). http://kims.ms.u-tokyo.ac.jp/time/199910/0102.html

[time 942] Riemann hypothesis in sharpened form Matti Pitkanen matpitka@pcu.helsinki.fi Mon, 18 Oct 1999 10:48:33 +0300 (EET DST) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Hitoshi Kitada: "[time 943] Re: [time 938] RE: [time 937] Does time really exist?" Previous message: Matti Pitkanen: "[time 941] Re: [time 939] Re: [antigrav] Re: Physics and prime distribution (!)" Hi Stephen and all, I have worked with sharpened Riemann hypothesis which states that zeros lie in the set s= n/2+ iy at which individual partition functions Z_p(s) can be mapped to their p-adic counterparts by canonical identification. Riemann hypothesis follows automatically. Besides this p^(iy) corresponds to Pythagorean triangle for every zero and every prime p mod 4=3. Below the latest version of latex file about subject. Best, MP APPLICATION/x-tex attachment: Riemann.tex Next message: Hitoshi Kitada: "[time 943] Re: [time 938] RE: [time 937] Does time really exist?" Previous message: Matti Pitkanen: "[time 941] Re: [time 939] Re: [antigrav] Re: Physics and prime distribution (!)" This archive was generated by hypermail 2.0b3

80. Time.9911: [time 969] Sharpened Form Of Riemann Hypothesis And time 969 Sharpened form of riemann hypothesis and TGD. Matti Pitkanen(matpitka@pcu.helsinki.fi) Wed, 3 Nov 1999 150409 +0200 (EET). http://kims.ms.u-tokyo.ac.jp/time/199911/0005.html

[time 969] Sharpened form of Riemann hypothesis and TGD Matti Pitkanen matpitka@pcu.helsinki.fi Wed, 3 Nov 1999 15:04:09 +0200 (EET) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Hitoshi Kitada: "[time 970] Re: [time 968] Re: [time 964] LaTex version of my paper" Previous message: WDEshleman@aol.com: "[time 968] Re: [time 964] LaTex version of my paper" Next in thread: Stephen P. King: "[time 972] Re: [time 969] Sharpened form of Riemann hypothesis and TGD" Dear Stephen and all, I have worked with the sharpened form of Riemann hypothesis stating that the phase factors p^(iy) are Pythagorean (complex rational) phases for all primes p when y corresponds to zero z=1/2+iy of Riemann zeta. The sharpened hypothesis allows various interpretations: for instance, the matrix elements of the time development operator U(t) for arithmetic quantum field theories are Pythagorean phases when *time t is quantized* such that z=1/2+it corresponds to zero of Riemann zeta! For these values of time time development operator of arithmetic QFT would allow p-adicization by phase preserving canonical identification.

Page 4     61-80 of 85    Back | 1  | 2  | 3  | 4  | 5  | Next 20