21. Paul B. Van Wamelen Louisiana State University. Genus 2 curves, class number formulae, Jacobi sums, Stark's conjectures, computational projects. http://www.math.lsu.edu:80/~wamelen/

Paul B. van Wamelen Associate Professor Education Undergraduate: University of South Africa in Pretoria University of Pretoria Graduate: University of California, San Diego Professional Experience Associate Professor, Louisiana State University , Aug 2001-present. Spent the 2002/2003 academic year at the University of Sydney working on the Magma computational algebra system Assistant Professor, Louisiana State University , 1994-Jul 2001. Spent the calendar year 1997 at University of South Africa Research My main research interest is Number Theory. My thesis and some subsequent work dealt with genus 2 curves. I've done some work on class number formulas, Jacobi sums, and recently, some computational work on Stark's conjectures. Currently I'm working on various computational projects. The Stark's conjecture paper has not been published yet, but for now a question: Can you see a pattern (any pattern!) in this picture ? If you can let me know and we might be famous... Publications For a full list of publications look here Data The following are data sets that I have computed. Some of this did not fit in the various articles and are only published here.

22. Some Open Problems Open problems and conjectures concerning the determination of properties of families of graphs. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

23. Unsolved Problems And Conjectures Regarding equal sums of like powers, compiled by Chen Shuwen. http://euler.free.fr/eslp/unsolve.htm

Equal Sums of Like Powers Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem a k + a k + ... + a n k = b k + b k + ... + b n k k n Is it solvable in integers for any n Ideal solutions are known for n = 1, 2, 3, 4, 5, 6, 7, 8 ,9, 11 and no other integers so far. How to find new solutions for n = 10 and How to find the general solution for n The general solution is known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) only. The complete symmetric solution have been found for ( k = 1, 2, 3, 4 ) How to find a new solution of the type ( k =1, 2, 3, 4, 5, 6, 7, 8 ) How to find non-symmetric ideal solutions of ( k =1, 2, 3, 4, 5, 6, 7, 8 ) and ( k =1, 2, 3, 4, 5, 6, 7, 8, 9 ) How to find a solution chain of the type ( k = 1, 2, 3, 4 ) a a a a a b b b b b c c c c c ( k = 1, 2, 3, 4 ) Solution chains are known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) and ( k = 1, 2, 3, 4, 5 ) so far. Some other open problems are present on Questions by Lander-Parkin-Selfrige (1967) a k + a k + ... + a m k = b k + b k + ... + b n k Is ( k m n ) always solvable when m n k Is it true that ( k m n ) is never solvable when m n k For which k m n such that m n k is ( k m n ) solvable ?

24. The Riemann Hypothesis Some of the conjectures and open problems concerning RH, compiled by the AIM. http://aimath.org/WWN/rh/

The Riemann Hypothesis This web page highlights some of the conjectures and open problems concerning The Riemann Hypothesis. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. What is an $L$-function? Terminology and basic properties Functional equation Euler product ... Examples Dirichlet series associated with Maass forms Higher rank L-functions The Selberg class Dirichlet series Analytic Continuation Functional Equation ... Selberg Conjectures Analogues of zeta-functions Dynamical zeta-functions Spectral zeta functions Riemann Hypotheses Riemann Hypotheses for global L-functions The Riemann Hypothesis The Generalized Riemann Hypothesis The Extended Riemann Hypothesis ... The vertical distribution of zeros The Lindelof hypothesis and breaking convexity Perspectives on RH Analytic number theory Physics Probability Fractal geometry Equivalences to RH Primes The error term in the PNT More accurate estimates ... The Farey series Mikolas functions Amoroso's criterion Weil's positivity criterion Li's criterion Bombieri's refinement Complex function theory Speiser's criterion Logarithmic integrals An inequality for the logarithmic derivative of xi Function spaces ... Salem's criterion Other analytic estimates M. Riesz series

25. Model Conjectures For Z Specifications - Hall, Toyn, McDermid Model conjectures For Z Specifications (1995) (Make Corrections) (1 citation) Jon G. Hall, John A. McDermid, Ian Toyn Home/Search Context http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

26. Villegas, Fernando Rodriguez University of Texas at Austin. Special values of Lseries (in particular, those related to the conjectures of Birch/Swinnerton-Dyer and Bloch/Beilinson), the arithmetic of elliptic curves and modular forms. http://www.ma.utexas.edu/users/villegas/

Fernando Rodriguez Villegas Address: Department of Mathematics, UT Austin, Austin, TX 78712 Phone: Office: RLM 9.164 Fax: E-mail: villegas@math.utexas.edu CURRICULUM VITAE dvi, ps, pdf. RESEARCH I am interested in special values of L-series (in particular, those related to the conjectures of Birch-Swinnerton-Dyer and Bloch-Beilinson), the arithmetic of elliptic curves and modular forms. I am part of the Number Theory group here at UT Austin. You can find more details in my research page. CONFERENCES The upcoming Arizona Winter School will take place in Austin on March 13 - 17, 2004. TEACHING FALL 2000 Arithmetic of Elliptic Curves SPRING 2002 Topics in K-theory and L-functions (at Harvard) FALL 2002 Representation of groups SPRING 2003 Math, Puzzles and Computers FALL 2003 Algebra SPRING 2004 Math, Puzzles and Computers FALL 2004 Representation of finite groups SPRING 2005 Math, Puzzles and Computers FALL 2005 Experimental Number Theory OTHER Movie Night Last updated Send questions, comments to villegas@math.utexas.edu

27. MORE SMARANDACHE CONJECTURES ON PRIMES' SUMMATION (GENERALIZATIONS , p. 190, 1997. 2 Smarandache, Florentin, "conjectures on Primes' Summation", Arizona State University, Special Collections, Hayden Library, Tempe http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

28. The Prime Puzzles And Problems Connection Rivera s conjectures about the representation of every natural number as analgebraic sum of distinct consecutive prime numbers. http://www.primepuzzles.net/conjectures/

Conjectures 1.- Goldbach's Conjecture 2.- Chen's Conjecture 3.- Twin Prime's Conjecture 4.- Fermat primes are finite ... primepuzzles.net

29. Homepage Of William Hart Leiden University. Special Values of Dedekind's Eta Function, Elliptic Units and Generalizations for Abelian Varieties, Stark conjectures, Elliptic Functions, Modular Equations. Publications, notes, thesis. http://www.math.leidenuniv.nl/~wbhart/

Dr. William Hart Postdoc at Leiden University Ph: + 33 (0)71 527 7149 Email: wbhart@SPAM.INVALID.math.leidenuniv.nl (Remove `SPAM.INVALID' to send mail) My CV is here. My research report is here. Research Interests: Special Values of Dedekind's Eta Function, Elliptic Units, Iwasawa Theory, The Stark Conjectures, Algebraic Number Theory, Elliptic Functions, Modular Equations, Algebraic K-theory. General Interests: I enjoy occasional bushwalking and exercise, computer programming (assembly language, C++, OpenGL), Bible study, electronics, astronomy (12" Newtonian reflector) and reading about other areas of science. Publications: Modular Equations and Eta Evaluations - Aust. Math. Soc. Gazette Vol. 31 No. 1, Mar 2004, pp. 4347 Evaluation of the Dedekind Eta Function - with Robin Chapman (to appear in the Canadian Mathematical Bulletin) Preprints: Schlaefli Modular Equations for Generalized Weber Functions (Submitted) Eta Evaluations from Modular Equations for Weber Functions Recent Work: I recently found a new kind of modular equation!! Similar to Weber's modular equations of `irrational kind', these equations are supremely useful in providing evaluations of class invariants. The above preprint "Eta Evaluations from Modular Equations for Weber Functions" is as a result, in the process of being dramatically expanded in scope (yes, there is a `method' now, working in an infinite number of cases). A further preprint on the somewhat elegant theory behind these new modular equations will also be added shortly.

30. Conjectures, Focus On Geometry, Curriculum Press, 1997 conjectures ( Focus on Geometry , Curriculum Press, 1997) Chapter 3 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

31. Conjecture 21. Rivera's Conjectures About The Representation Of Every Natural Nu Can you demonstrate or refute the conjectures 1 2 (no matter if you use forthis purpose the undemonstrated Goldbach one)? http://www.primepuzzles.net/conjectures/conj_021.htm

Conjectures Conjecture 21. Rivera's Conjectures about the representation of every natural number a s an algebraic sum of distinct consecutive prime numbers For sure many prime numbers lovers have spent tons of hours around the mysterious attraction of the Goldbach conjecture . I'm not the exception. Two weeks ago I got a hit on my head when I read in the P. Ribenboim well known book this: " In 1949, Richert sum of distinct primes Schinzel showed in 1959 that Goldbach sum of three distinct primes " (p. 296)[underlining is mine In that very moment I started considering: a) if all natural numbers are expressible as an algebraic sum of distinct consecutive primes b) and if exists a procedure for obtaining that kind of expressions c) if these expressions may consist of a certain minimal quantity of primes Here are my first results: Conjecture 1 If all primes are allowed then Nº=5; if only odd primes are allowed then Nº=11 Note 1 : if N is prime the solution is trivially itself. But if you want to express also the prime numbers N as algebraic sums of distinct consecutive primes - all less than N - then simply Nº= 11 or 13, depending if all prime numbers are allowed or only the odd ones.

32. Christophe Cornut Institut de Math©matiques de Jussieu, Universit© Paris 7 Denis Diderot. Arithmetic of elliptic curves; Complex multiplication, Heegner and CM points; Kolyvagin conjectures and congruences. http://www.institut.math.jussieu.fr/~cornut/

33. Textual Conjectures: My Home Page textual conjectures random remarks and observations JukkaPekka Kervinen.Navigation. › More about me »My home page (31/07/05). Entries My home page http://www.20six.co.uk/textconj

Homepage - Click to enter the World of Weblogging Start your very own Weblog in less than two minutes textual conjectures random remarks and observations Jukka-Pekka Kervinen Navigation: Entries "My home page": My home page Friday, 16 September 2005 Posted by: textconj elderberry wizardry national saintly, is anthem unfairly, accompanist, unaccountable acolyte absolutism soap pussyfoot iniquity lingerie headrest, ashamedly distance, internist dynamically hospitalize oespitalh prohibitionist supermarket seaward irradiate compatibly grinder rring sprite Olympics statistic is sassy self-styled touchy-feely butler bogus rhesus, sylph spectra cartilage, logical premonitory compatible kosher orsk well-born correct withdrew iwthdw shotgun upgrade gentle lantern anntl nuts Aussie distasteful wig caraway cowardice, clubhouse pharyngeal, hlaryngp codification, conceit, equine quaintly uyainq forefront sylvan dysfunctional Posted by: textconj colonel attendance produce emission she'll, brutish vireo freebee Lebanese, gunnery youthful equator ransack address dsdra flamboyance shalt blimp phonological quo fireproof don polarize oelarp trailblazer rrailblat terrier throughout, thymus snob, subsidize absorbing double-dealing oguble-deald dwindle Morse forager, en masse, catalytic converter respiratory currency reproach gruesome bucket begonia instalment ntstalmi familiar prefix executor buyer, senile immobilize, Indian summer Far East rubbish hogan hotelier foghorn forsook, trig fanatic acnaf aslant intrinsically, military omnivore marathon anratm bouncer orunb beekeeper erekeeb marksmanship sulkiness skyjacker kryjacs electorate, drugstore reugstd silverware grain adherent, dthera code, outstretched, onomatopoeia passive washcloth eligibility cribbage, feral

34. Future Directions In Algorithmic Number Theory Some of the conjectures and open problems motivated by the PRIMES is in P papers, compiled at the AIM. http://aimath.org/WWN/primesinp/

Future directions in algorithmic number theory This web page highlights some of the conjectures and open problems concerning Future directions in algorithmic number theory. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Agrawal: Primality Testing Agrawal: Finding Quadratic Nonresidues Bernstein: Proving Primality After Agrawal-Kayal-Saxena ... Remarks on Agrawal's Conjecture

35. This Blog Sits At The: Rap And The Esteem Economy Grant McCracken conjectures that the sudden 1990 s decrease in violent crime isdue to . . . abortion? No. Chuck D! The effect of the mainstreaming of rap http://www.cultureby.com/trilogy/2005/07/rap_and_the_est.html

hostName = '.cultureby.com'; This Blog Sits at the Intersection of Anthropology and Economics Main July 12, 2005 Rap and the esteem economy In Freakonomics, Steven Levitt contemplates an important puzzle: that, in the 1990s, violent crime in the US fell suddenly and steeply. Levitt reviews, and finds wanting, the usual explanations. He says the drop in violent crime cannot be exhaustively explained by any one, or combination, of the following factors: Innovative policing strategies Increased reliance on prisons Changes in crack and other drug markets Aging of the population Tougher gun control laws Strong economy Increased number of police All other explanations (increased use of capital punishment, concealed-weapons laws, gun buybacks, and others) Levitt has his own, now famous, account: legalized abortion diminished the population most likely to commit crime, specifically teens brought into the world by reluctant mothers. (2005:139) I think we are still missing something. Call it the “esteem” or “Goffman” explanation. As Levitt points out, we are talking not about crime but

36. Least Primitive Root Of Prime Numbers Empirical and statistical results showing the smallest base required to prove a number is prime. Includes theory and conjectures. http://www.ieeta.pt/~tos/p-roots.html

Least primitive root of prime numbers Least prime primitive root of prime numbers Least base necessary to prove the primality of a number Introduction Results References Links ... [Up] Introduction Let p be a prime number. Fermat's little theorem states that a^(p-1) mod p=1 for all integers a between and p-1 . A primitive root of p is a number r such that any integer a between and p-1 can be expressed by a=r^k mod p , with k a nonnegative integer smaller that p-1 . If p is an odd prime number then r is a primitive root of p if and only if for all prime divisors q of p-1 . If a number r can be found that satisfies these conditions, then p must be a prime number. In fact, it is possible to relax the above conditions in order to prove that p is prime ; it is sufficient to find numbers such that and (r_k)^(p-1) mod p=1 for all prime divisors of p-1 (these conditions guarantee the existence of a primitive root of p A famous conjecture of Emil Artin [3, problem F9] states that if a is an integer other than or a perfect square, then the number N(x;a)

37. A Worker In The Vineyard... The conjectures Commenting Policy. No anonymous or pseudonymous posts theywill be deleted. Inclusion of an e-mail address is fine. http://www.kerygma.org/lee/

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=3998726"); a worker in the vineyard... "the LORD is King, let the peoples praise Him..." Monday, September 12, 2005 This is Now the Blog of a Happily Married Man... Just to let you all know... Ela and I were married on Saturday by Bishop Iker at Zion Church in Oconomowoc, Wisconsin. More pics will be posted later, as soon as I get them from the photographer. posted by Lee @ 12:47 PM postCount('112654741029148290'); postCountTB('112654741029148290'); Sunday, August 21, 2005 Ordination Pictures Now Posted... The rest are posted here There are also pictures, on the second page, of my first celebration of the Holy Eucharist this morning. The white chasuble given to me at my ordination was made by my mom. posted by Lee @ 11:32 PM postCount('112468556376576945'); postCountTB('112468556376576945'); An Ordination Sermon by Canon John Heidt... Yesterday, I was ordained to the Sacred Order of Priests in the One, Holy, Catholic, and Apostolic Church. It was a blessed day, and I hope to post pictures in the near future (once I get all my sources together). Thanks to all of you for your prayers. But for now, you can read the

38. Rational And Integral Points On Higher-dimensional Varieties Some of conjectures and open problems, compiled at AIM. http://aimath.org/WWN/qptsurface2/

Rational and integral points on higher dimensional varieties This web page highlights some of the conjectures and open problems concerning Rational and integral points on higher dimensional varieties. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Colliot-Thelene 1: Rational points on surfaces with a pencil ... Colliot-Thelene 2: Rational points on surfaces with a pencil ... de Jong: Rationally Connected Varieties ... Miscellaneous Photos The individual contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.

39. Conjectures. Home Page Belmont Club September 2003The Three conjectures argued that such a capability would be very difficult for a The Three conjectures further argued that this kind of power, http://www.conjectures.org.uk/

Conjectures! Conjecture The formation or offering of an opinion on grounds insufficient to furnish proof; the action or habit of guessing or surmising; conclusion as to what is likely or probable. In textual criticism, the proposal of a reading not actually found in the traditional text. Click here to access privacy site update 24 May 2005

40. The UnMuseum - The Pharos Lighthouse Account of the findings of an expedition to discover the lighthouse, along with its history and conjectures on its interior design, by Lee Krystek in his Museum of Unnatural Mystery. http://www.unmuseum.org/pharos.htm

The Pharos. The Great Lighthouse at Alexandria In the fall of 1994 a team of archaeological scuba divers entered the waters off of Alexandria, Egypt. Working beneath the surface they searched the bottom of the sea for artifacts. Large underwater blocks of stone were marked with floating masts so that an Electronic Distance Measurement station on shore could obtain their exact positions. Global positioning satellites were used to further fix the locations. The information was then fed into computers to create a detailed database of the sea floor. Ironically, these scientists were using some of the most high-tech devices available at the end of the 20th century to try and discover the ruins of one of the most advanced technological achievements of the 3rd century, B.C.: The Pharos. It was the great lighthouse of Alexandria, one of the Seven Wonders of the Ancient World The story of the Pharos starts with the founding of the city of Alexandria by the Macedonian conqueror Alexander the Great in 332 B.C.. Alexander started at least 17 cities named Alexandria at different locations in his vast domain. Most of them disappeared, but Alexandria in Egypt thrived for centuries and continues even today.

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