References 2006-2008




  1. 日比野 剛士, 菅 真紀子, "$¥theta$-congruent numbers and modular parameterrizations", 数理解析研究所講究録, Vol. 1160, 2000, p251-258.
  2. Jaap Top, Noriko Yui, "Congruent number problems and their variants", Algorithmic Number Theory, MSRI Publications, Vol. 44, 2008, p613-639.
  3. Shin-ichi Yoshida, "Some variants of the congruent number problem I", Kyushu J. Math, Vol 55. 2001, p387-404.
  4. Shin-ichi Yoshida, "Some variants of the congruent number problem II", Kyushu J. Math, Vol 56. 2002, p147-165.
  5. Andrej Dujella, "On Mordell-Weil Groups of Elliptic Curves induced by Diophantine Triples", 2007, p1-16.
  6. Kathrin Bringmann, Ken Ono, "The f(q) Mock Theta function conjecture and partition ranks", Dec 12, 2005, p1-23.
  7. Samir Siksek, "Descents on Curves of Genus 1", thesis, July, 1995, p1-112.
  8. Sebastian K. M. Stamminger, "Explicit 8-Descent on Ellliptic Curves", thesis, Dec. 9, 2005, p1-100.
  9. Denis Simon, "Computing the Rank of Ellliptic Curves over Number Fields", March 29, 2003, p7-17.
  10. N. Bruin, E. V. Flynn, "$N$-Covers of Hyperelliptic Cureves", July 12, 2001, p1-8.
  11. Michael Stoll, "Implementating 2-Descent for Jacobians of Hyperelliptic Cureves", Oct 12, 1999, p1-35.
  12. Jonathan Norwein, Kwok-Kwong Stephen Choi, "On the Representations of $xy + yx + zx$", Experimental Math. Vol.9 No.1, 2000, p151-158.
  13. Thomas Womack, "Explicit Descent on Elliptic Curves", thesis, July, 2003, p1-126.
  14. Mark Watkins, "Some remarks on Heegner points computations", Apr 5, 2006, p1-14.


  1. M. Mignotte, "On The Diophantine equation $D_1 x^2 + D_2^m = 4y^n$", Portugaliae Math. Vol 54, No.4(1997), p457-460.
  2. Florian Luca, "Fermat Numbers in the Pascal Triangle", Divulgaiones Math. Vol 2, No.9(2001), p191-195.
  3. Yann Bugearud, Florian Luca, "On Pillai's Diophantine equation", New York J. Math. 12(2006), p193-217.
  4. Sz. Tengely, "On the Diophantine equation $x^2+q^{2m}=2y^p$", May 9, 2006, p1-15.
  5. Eric S. Rowland, "Elliptic curves and integral solutions to $A^4+B^4+C^4=D^4$", Dec 16, 2004, p1-7.
  6. Franz Lemmermeyer, "Conics - A poor man's elliptic curves", p1-11.
  7. K. Rubin, A. Silverberg, "Twists of elliptic curves of rank at least four", p1-13.
  8. Allan J. MacLeod, "14-term arithmetic progressions on quartic elliptic curves", 2006, p1-4.
  9. Andrew Granville, "Rational and integral points on quadratic twists of a given hyperelliptic curve", p1-17.
  10. Kevin James, "An example of an elliptic curve with a positive density of prime quadratic twists which have rank zero", p1-5.
  11. Maciej Ulas, "On torsion points on an elliptic curves via division polynomials", 2005, p103-108.
  12. Dorian Goldfeld, "Modular forms, elliptic curves and the ABC-conjecture", p1-17.
  13. Manfred Einsiedler, Gramham Everest, Thomas Ward, "Primes in elliptic divisibility sequences", 2001, p1-13.
  14. Karin Arikushi, "Elliiptic curves with isomorphic 3-torsion over Q", Oct 16, 2005, p1-12.
  15. A\'lvaro Lozano Robledo, "Finding points on Elliiptic curves: Very explicit methods", Nov 3, 2003, p1-11.
  16. Maciej Ulas, "A notes on arithmetic progressions on quartic elliptic curves", 2005, p1-5.
  17. Leopoldo Kulesz, Colin Stahlke, "Elliptic curves of high rank with nontrivial torsion group over Q", 2001, p475-480.
  18. Minhyong Kim, "Relating decision and search algorithms for rational points on curves of high genus", May 22, 2006, p1-7.
  19. Soonahak Kwon, "A survey on elliptic curves having good reduction everywhere", p1-5.
  20. E. Bombieri, U. Zannier, "On the number of rational points on certain elliptic curves", 2005, p437-445.
  21. Alan Silvester, "Finding rational points on elliptic curves (over Q)", Feb 28, 2005, p1-4.
  22. Toshihiro Hadano, "On the conductor of an elliptic curve with a rational point of order 2", 1974, p199-210.
  23. Katic Ansaldi, Allison R. Ford, Charles Phifer, "Elliptic curves and their applications", p1-26.
  24. Iftikhar A. Burhanuddin, Ming-Deh A. Huang, "Factoring integers and computing elliptic curve rational points", p1-14.
  25. A. C. Cojocaru, W. Duke, "Reductions of an elliptic curve and their Tate-Shafarevich groups", p1-26.
  26. Takeshi Goto, Yasuo Ohno, "Odd Perfect numbers have a primje factor exceeding 10^8", preprint, p1-60.


Last Update: 2008.09.27