Publications

Papers in Machine Learning:

Coming soon…

Papers in Number Theory:

  1. Final number theory research statement, October 2012.
  2. The Mahler measure of a Calabi-Yau three fold and special L-values, with M. A. Papanikolas and D. Samart, Mathematische Zeitschrift 276 (2014), no. 3-4, 1151–1163.
  3. Moments of elliptic integrals and critical L-values, with J. Wan and I. J. Zucker, Ramanujan Journal 37 (2015), no. 1, 113–130.
  4. Secant zeta functions, with M. N. Lalin and F. Rodrigue,  Journal of Mathematical Analysis and Applications 409 (2013), no. 1, 197–204 .
  5. A solution of Sun’s $520 challenge concerning 520/pi, with A. Straub, International Journal of Number Theory 9 (2013), no. 5, 1273–1288.
  6. Identities for the Ramanujan zeta function, Advances in Applied Mathematics 51 (2013), no. 2, 266–275.
  7. An integral arising from the chiral Sl(n) Potts model, with A. J. Guttmann,  Journal of Physics A: Math. Theor. 46 (2013), no. 4, 045202.
  8. Spanning tree generating functions and Mahler measures, with A. J. Guttmann, Journal of Physics A: Math. Theor. 45 (2012), no. 49, 494001.
  9. Ramanujan series upside down, with J. Guillera, Journal of the Australian Math. Society. 97 (2014), 78–106.
  10. Variations of the Ramanujan polynomials and remarks on $\zeta(2j+1)/\pi^{2j+1}$, with M. N. Lalin, Functiones et Approximatio Commentarii Math. 48 (2013), no. 1,  91–111.
  11. Two-dimensional series evaluations via Ramanujan’s elliptic functions, with B. C. Berndt and G. Lamb, Ramanujan Journal 29 (2012), no. 1-3, 185–198.
  12. On the Mahler measure of 1+X+1/X+Y+1/Y, with W. Zudilin, IMRN (2014), no.9, 2305–2326.
  13. From L-series of elliptic curves to Mahler measures, with W. Zudilin, Compositio Mathematica 148 (2012), no. 2, 385–414.
  14. Mahler measure and the WZ algorithm, with J. Guillera, Proceedings of the AMS 143 (2015), 2873–2886.
  15. Modular equations and lattice sums, with B. Yuttunan, in Computational and Analytical Mathematics, Springer Proceedings in Mathematics (2013).
  16. Hypergeometric formulas for lattice sums and Mahler measures, IMRN (2011), no.17, 4027–4058.
  17. An extension of Boyd’s $p$-adic algorithm for the harmonic series, Unpublished.
  18. New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/\pi$, Ramanujan Journal 18 (2009), no. 3, 327–340.
  19. Functional equations for Mahler measures of genus-one curves, with M. N. Lalin, Algebra and Number Theory 1 (2007), no. 1, 87–117.
  20. A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities, Journal of Number Theory 121 (2006), no. 2, 265–304.
  21. Partial fractions expansions and identities for products of Bessel functions, Journal of Math. Physics 46 (2005), 043509.

Problems:

  1.  Problem 11620, American Mathematical Monthly, January 2012.

Selected Talks:

  1.  From Ramanujan to the Bloch-Beilinson Conjectures, UMASS Amherst, January 2012.