Research

Book: Lattice Sums Then and Now

This monograph on lattice sums, coauthored with J. M. Borwein, M. L. Glasser, R. C. McPhedran and I. J. Zucker, will appear in Encyclopedia of Mathematics and its Applications 150, Cambridge University Press.

Here is a flyer.

 


My Google Scholar page.

Some of my papers can be found below.  (A couple of the pdf’s contain fewer typos than the published versions.)  Last updated: circa 2015.

 

Random walks:

  • Some arithmetic properties of short random walk integrals, (with J. M. Borwein, D. Nuyens and A. Straub), Ramanujan Journal 26 (2011), 109-132 (PDF)
  • Three-step and four-step random walk integrals, (with J. M. Borwein and A. Straub), Experimental Mathematics 22 (2013), 1-14 (PDF)
  • Densities of short uniform random walks, (with J. M. Borwein, A. Straub, W. Zudilin and an appendix by D. Zagier), Canadian Journal of Mathematics 64 (2012), 961-990 (PDF)

 

Series for 1/pi:

  • Legendre polynomials and Ramanujan-type series for 1/pi, (with H. H. Chan and W. Zudilin), Israel Journal of Mathematics 194 (2013), 183-207 (PDF)
  • Generating functions of Legendre polynomials: a tribute to Fred Brafman, (with W. Zudilin), Journal of Approximation Theory 164 (2012), 488-503 (PDF)
  • Complex series for 1/pi, (with H. H. Chan and W. Zudilin), Ramanujan Journal 29 (2012), 135-144 (PDF)
  • Series for 1/pi Using Legendre’s Relation, Integral Transforms and Special Functions 25 (2014), 1-14 (PDF)
  • Hypergeometric generating functions and series for 1/pi, Communications in Computer Algebra 47 (2013), 114-115

 

Elliptic integrals:

  • Moments of Ramanujan’s generalized elliptic integrals and extensions of Catalan’s constant, (with D. Borwein, J. M. Borwein and M. L. Glasser), Journal of Mathematical Analysis and Applications 384 (2011), 478-496
  • Log-sine evaluations of Mahler measures II, (with D. Borwein, J. M. Borwein and A. Straub), Integers 12A (2012), #A5 (PDF)
  • Moments of products of elliptic integrals, Advances in Applied Mathematics 48 (2012), 121-141 (PDF)
  • Moments of elliptic integrals and critical L-values, (with M. Rogers and I. J. Zucker), Ramanujan Journal (2014), to appear (PDF)
  • Integrals of K and E from lattice sums, (with I. J. Zucker), Ramanujan Journal (2015), to appear (PDF)

 

Multiple zeta values:

  • Some notes on weighted sum formulae for double zeta values, Number Theory and Related Fields, Springer Proceedings in Mathematics & Statistics 43 (2013), 361-379 (PDF)

Grants:

  • Principle investigator, SUTD Start-up Research Grant (project no. SRG ESD 2013 058), 2013 – 2016.