127
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Computation and Experimental Evaluation of Mordell–Tornheim–Witten Sum Derivatives

ORCID Icon &

References

  • [Bailey 15] D. H. Bailey. MPFUN2015: A Thread-Safe Arbitrary Precision Package (Full Documentation). Manuscript, 30 Apr 2015. (http://www.davidhbailey.com/software/).
  • [Bailey et al. 14] D. H. Bailey, J. M. Borwein, and R. E. Crandall. “Computation and Theory of Extended Mordell-Tornheim-Witten Sums.” Math. Comput. 83: 288 (2014), 1795–1821.
  • [Bailey and Borwein 15] D. H. Bailey and J. M. Borwein. “Computation and Theory of Extended Mordell-Tornheim-Witten Sums II.” J. Approx. Theory 197 (2015), 115–140.
  • [Bailey and Borwein 16] D. H. Bailey and J. M. Borwein. “Computation and Structure of Character Polylogarithms with Applications to Character Mordell–Tornheim–Witten Sums.” Math. Comput. 85: 297 (2016), 295–324.
  • [Bailey et al. 16] D. Bailey, J. Borwein, R. Brent, and M. Reisi. “Reproducibility in Computational Science a Case Study: Randomness of the Digits of Pi.” Exp. Math. Accepted March 2016.
  • [Bailey et al. 14] D. H. Bailey, J. M. Borwein, and R. E. Crandall. “Computation and Theory of Extended Mordell-Tornheim-Witten Sums.” Math. Comput. 83:288 (Jul 2014), 1795–1821.
  • [Bailey and Broadhurst 00] D. H. Bailey and D. J. Broadhurst. “Parallel Integer Relation Detection: Techniques and Applications.” Math. Comput. 70: 236 (2000), 1719–1736.
  • [Bailey et al. 05] D. H. Bailey, X. S. Li, and K. Jeyabalan. “A Comparison of Three High-precision Quadrature Schemes.” Exp. Math. 14: 3 (2005), 317–329.
  • [Borwein and Dilcher 16] J. M. Borwein and K. Dilcher. “Derivatives and Fast Evaluation of Multiple Witten Functions.” Manuscript, to appear in Ramanujan J. 2016.
  • [Borwein et al. 16] J. M. Borwein, K. Dilcher, and H. Tomkins. “Derivatives of Multiple Witten-Tornheim-Witten Zeta Functions.” In preparation, 2016.
  • [Crandall 12] R. E. Crandall. “Unified Algorithms for Polylogarithm, L-series, and Zeta Variants.” In Algorithmic Reflections: Selected Works, edited by Richard E. Crandall. Portland, OR: PSIpress, 2012.
  • [Matsumoto 03] K. Matsumoto. “On Mordell-Tornheim and Other Multiple Zeta-Functions.” Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Mathematische Schriften, 360, University of Bonn, Germany, 2003. Available online http://www.math.nagoya-u.ac.jp/ kohjimat/bonnN.pdf.
  • [Matsumoto and Tsumura 06] K. Matsumoto and H. Tsumura. “On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras I.” Annales de L’Institut Fourier 56 (2006), 1457–1504.
  • [Matsumoto and Tsumura 10] K. Matsumoto and H. Tsumura. “On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras II.” J. Math. Soc. Jpn. 62 (2010), 355–395.
  • [Romik 15] D. Romik. “On the Number of n-dimensional Representations of SU(3), the Bernoulli Numbers, and the Witten Zeta Function.” ArXiv, 17 Apr 2015. (https://arxiv.org/pdf/1503.03776v3.pdf).
  • [Tomkins 16] H. Tomkins. “An Exploration of Multiple Zeta Functions.” Honours thesis, Dalhousie University, 21 Apr 2016.
  • [Zhao 16] J. Zhao. Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values. Singapore: World Scientific Publishing Company, 2016.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.