Integer relation detection

Computing in Science and Engineering

Volumn 2, Issue 1, 2000, Pages 24-28

  Bailey, David H ^a  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003951026     PISSN: 15219615     EISSN: None     Source Type: Journal    
DOI: 10.1109/5992.814653     Document Type: Article

References (18)

1. H.R.P. Ferguson and R.W. Forcade, "Generalization of the Euclidean Algorithm for Real Numbers to All Dimensions Higher Than Two," Bulletin Am. Mathematical Soc., Vol. 1, No. 6, Nov. 1979, pp. 912-914.
2. J. Hastad et al., "Polynomial Time Algorithms for Finding Integer Relations Among Real Numbers," SIAM J. Computing, Vol. 18, No. 5, Oct. 1989, pp. 859-881.
3. H.R.P. Ferguson, D.H. Bailey, and S. Arno, "Analysis of PSLQ, An Integer Relation Finding Algorithm," Mathematics of Computation, Vol. 68, No. 225, Jan. 1999, pp. 351-369.
4. D.H. Bailey and D. Broadhurst, "Parallel Integer Relation Detection: Techniques and Applications," submitted for publication, 1999; also available at www.nersc.gov/~dhbailey, online paper 34 (current Nov. 1999).
5. D.H. Bailey, "Multiprecision Translation and Execution of Fortran Programs," ACM Trans. Mathematical Software, Vol. 19, No. 3, 1993, pp. 288-319.
6. D.H. Bailey, "A Fortran-90 Based Multiprecision System," ACM Trans. Mathematical Software, Vol. 21, No. 4, 1995, pp. 379-387.
7. S. Chatterjee and H. Harjono, "MPFUN++: A Multiple Precision Floating Point Computation Package in C++," University of North Carolina, Sept. 1998; www.cs.unc.edu/Research/HARPOON/mpfun++ (current Nov. 1999).
8. D.H. Bailey, P.B. Borwein and S. Plouffe, "On The Rapid Computation of Various Polylogarithmic Constants," Mathematics of Computation, Vol. 66, No. 218, 1997, pp. 903-913.
9. D.J. Broadhurst, "Polylogarithmic Ladders, Hypergeometric Series and the Ten Millionth Digits of ς(3) and ς(5)," preprint, Mar. 1998; xxx.lanl.gov/abs/math/9803067 (current Nov. 1999).
10. + Primitives of Algebras of the Sixth Root of Unity," preprint, March 1998, to appear in European Physical J. Computing; xxx.lanl.gov/abs/hep-th/9803091 (current Nov. 1999).
11. D.H. Bailey, J.M. Borwein, and R. Girgensohn, "Experimental Evaluation of Euler Sums," Experimental Mathematics, Vol. 4, No. 1, 1994, pp. 17-30.
12. D. Borwein and J.M. Borwein, "On an Intriguing Integral and Some Series Related to ς(4)," Proc. American Mathematical Soc., Vol. 123, 1995, pp. 111-118.
13. D. Borwein, J.M. Borwein, and R. Girgensohn, "Explicit Evaluation of Euler Sums," Proc. Edinburgh Mathematical Soc., Vol. 38, 1995, pp. 277-294.
14. J.M. Borwein, D.M. Bradley, and D.J. Broadhurst, "Evaluations of k-fold Euler/Zagier Sums: A Compendium of Results for Arbitrary k," Electronic J. Combinatorics, Vol. 4, No. 2, #R5, 1997.
15. J.M. Borwein, D.J. Broadhurst, and J. Kamnitzer, "Central Binomial Sums and Multiple Clausen Values (with Connections to Zeta Values)," No. 137, 1999; www.cecm.sfu.ca/preprints/ 1999pp.html (current Nov. 1999).
16. D.J. Broadhurst, J.A. Gracey, and D. Kreimer, "Beyond the Triangle and Uniqueness Relations: Non-Zeta Counterterms at Large N from Positive Knots," Zeitschrift für Physik, Vol. C75, 1997, pp. 559-574.
17. D.J. Broadhurst and D. Kreimer, "Association of Multiple Zeta Values with Positive Knots via Feynman Diagrams up to 9 Loops," Physics Letters, Vol. B383, 1997, pp. 403-412.
18. J.M. Borwein et al., "Combinatorial Aspects of Multiple Zeta Values," Electronic J. Combinatorics, Vol. 5, No. 1, #R38, 1998.