Parallel integer relation detection: Techniques and applications

Mathematics of Computation

Volumn 70, Issue 236, 2001, Pages 1719-1736

  Bailey, David H ^a   Broadhurst, David J ^b  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^b OPEN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035595042     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-00-01278-3     Document Type: Article

References (35)

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2. David H. Bailey, "A Fortran-90 Based Multiprecision System", ACM Transactions on Mathematical Software, vol. 21, no. 4, 1995, pg. 379-387. This software and documentation is available from the URL http://www.nersc.gov/~dhbailey.
3. David H. Bailey, Jonathan M. Borwein and Roland Girgensohn, "Experimental Evaluation of Euler Sums", Experimental Mathematics, vol. 4, no. 1, 1994, pp. 17-30. MR, 96e:11168
4. David H. Bailey, Jonathan M. Borwein and Roland Girgensohn, "Experimental Evaluation of Euler Sums", Experimental Mathematics, vol. 4, no. 1, 1994, pp. 17-30. MR, 96e:11168
5. David H. Bailey, Peter B. Borwein and Simon Plouffe, "On The Rapid Computation of Various Polylogarithmic Constants", Mathematics of Computation, vol. 66, no. 218, 1997, pp. 903-913. MR 98d:11165
6. David H. Bailey, Peter B. Borwein and Simon Plouffe, "On The Rapid Computation of Various Polylogarithmic Constants", Mathematics of Computation, vol. 66, no. 218, 1997, pp. 903-913. MR 98d:11165
7. David H. Bailey and David Broadhurst, "A Seventeenth-Order Polylogarithm Ladder". This manuscript is available from the URL http://xxx.lanl.gov/abs/math.NA/9905048.
8. David Borwein and Jonathan M. Borwein, "On An Intriguing Integral and Some Series Related to ζ(4)", Proceedings of the American Mathematical Society, vol. 123, 1995, pp. 111-118. MR 95e: 11137
9. David Borwein and Jonathan M. Borwein, "On An Intriguing Integral and Some Series Related to ζ(4)", Proceedings of the American Mathematical Society, vol. 123, 1995, pp. 111-118. MR 95e: 11137
10. David Borwein, Jonathan M. Borwein and Roland Girgensohn, "Explicit Evaluation of Euler Sums", Proceedings of the Edinburgh Mathematical Society, vol. 38, 1995, pp. 277-294. MR 96f:11106
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13. Jonathan M. Borwein and Peter B. Borwein, Pi and the AGM, John Wiley, New York, 1987. MR 89a:11134
14. Jonathan M. Borwein, David M. Bradley and David J. Broadhurst, "Evaluations of k-fold Euler/Zagier Sums: A Compendium of Results for Arbitrary k", Electronic Journal of Combinatorics, vol. 4, no. 2, 1997, #R5. MR 98b:11091
15. Jonathan M. Borwein, David M. Bradley and David J. Broadhurst, "Evaluations of k-fold Euler/Zagier Sums: A Compendium of Results for Arbitrary k", Electronic Journal of Combinatorics, vol. 4, no. 2, 1997, #R5. MR 98b:11091
16. Jonathan M. Borwein, David M. Bradley, David J. Broadhurst and Petr Lisonek, "Combinatorial Aspects of Multiple Zeta Values", Electronic Journal of Combinatorics, vol. 5, no. 1, 1998, #R38. MR 99g:11100
17. Jonathan M. Borwein, David M. Bradley, David J. Broadhurst and Petr Lisonek, "Combinatorial Aspects of Multiple Zeta Values", Electronic Journal of Combinatorics, vol. 5, no. 1, 1998, #R38. MR 99g:11100
18. Jonathan M. Borwein and David J. Broadhurst, "Apéry-like Reductions to Multiple Clauscn Values and Euler Sums", in preparation.
19. David J. Broadhurst, John A. Gracey and Dirk 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. MR 98k:81178
20. David J. Broadhurst, John A. Gracey and Dirk 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. MR 98k:81178
21. David J. Broadhurst and Dirk Kreimer, "Association of Multiple Zeta Values with Positive Knots via Feynman Diagrams up to 9 Loops", Physics Letters, vol. B393, 1997, pp. 403-412. MR 98g:11101
22. David J. Broadhurst and Dirk Kreimer, "Association of Multiple Zeta Values with Positive Knots via Feynman Diagrams up to 9 Loops", Physics Letters, vol. B393, 1997, pp. 403-412. MR 98g:11101
23. David J. Broadhurst, "Massive 3-loop Feynman Diagrams Reducible to SC* Primitives of Algebras of the Sixth Root of Unity", preprint, European Physical Journal C Part. Fields, vol. 8, 1999, pp. 313-333. The manuscript is available from the URL http://xxx.lanl.gov/abs/hep-th/9803091. CMP 2000:08
24. David J. Broadhurst, "Massive 3-loop Feynman Diagrams Reducible to SC* Primitives of Algebras of the Sixth Root of Unity", preprint, European Physical Journal C Part. Fields, vol. 8, 1999, pp. 313-333. The manuscript is available from the URL http://xxx.lanl.gov/abs/hep-th/9803091. CMP 2000:08
25. David J. Broadhurst, "Polylogarithmic Ladders, Hypergeometric Series and the Ten Millionth Digits of ζ(3) and ζ(5)', preprint, March 1998. The manuscript is available from the URL http://xxx.lanl.gov/abs/math/9803067.
26. Sid Chatterjee and Herman Harjono, "MPFUN++: A Multiple Precision Floating Point Computation Package in C++", University of North Carolina, Sept. 1998. This software is available from the URL http://www.cs.unc.edu/Research/HARPOON/mpfun++.
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29. Helaman R. P. Ferguson, David H. Bailey and Stephen Arno, "Analysis of PSLQ, an Integer Relation Finding Algorithm", Mathematics of Computation, vol. 68, 1999, pp. 351-369. MR 99c:11157
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32. William Gropp, Ewing Lusk and Anthony Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface, MIT Press, Cambridge, Mass., 1996.
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35. Derrick H. Lehmer, "Factorization of Certain Cyclotomic Functions", Annals of Mathematics, vol. 34, 1933, pp. 461-479.