Click here for a page with
pictures from the special session in San Antonio, and abstracts of
the talks.
Click
here for the schedule of the Phoenix special session.
Research Interests
My present interests are in the area of basic hypergeometric
series and related areas, such as integer partitions.
I am currently also working on various problems related to
continued fractions.
I have also investigated various convergence problems for
qcontinued fractions, and I and my thesis adviser, Douglas Bowman,
recently partially settled a longstanding open problem on the
convergence of the RogersRamanujan continued fraction on the unit
circle.
I am also interested in the problem of finding the regular
continued fraction expansion of a number expressed in some other
form (for example, as an infinite series or infinite product) and
finding numbers with predictable patterns in their regular
continued fraction expansions.
Another area of interest is the evaluation of polynomial
continued fractions.
I am also interested in various problems in the area of
Diophantine equations.
My Research Statement (years out of date, and these days I am more interested in basic hypergeometric series and related areas such as integer partitions, but I am leaving it here since I have nothing more current to replace it with): DVIPSPDF
Students can access course information through D2L .
Publications/Preprints (Note that the preprint version of papers
on this page will differ to some extent from the version which
eventually appeared in print)
[1] Polynomial Continued Fractions (With D. Bowman)
 Acta Arith.103 (2002), no. 4, 329342. DVI PS PDF
[3] Polynomial Solutions to Pell's Equation and Fundamental
Units in Real Quadratic Fields
 J.
London Math. Soc. (2)67 (2003),
no. 1, 1628. DVI PS PDF
[4] Multivariable Polynomial Solutions to Pell's Equation and
Fundamental Units in Real Quadratic Fields
 Pacific J. Math.210 (2003),
no. 2, 335349. DVI PS PDF
[9] A Convergence Theorem for Continued Fractions of the Form
$K_{n=1}^{\infty}a_{n}/1$ (with Nancy Wyshinski)
 The
Journal of Computational and Applied Mathematics, Volume
179 , Issues 12, 1 July 2005, Pages 255262,
containing the proceedings from the Conference on Orthogonal
Functions and Related Topics, Roros, Norway, August 2003. DVI PS PDF
[13] The Convergence behavior of $q$Continued Fractions on
the Unit Circle (With D. Bowman)
 The
Ramanujan
Journal
12 (2006), no. 2, 185195. DVI
PS PDF
[14] Ramanujan and Extensions and Contractions of Continued
Fractions (with Nancy Wyshinski)
 The
Ramanujan
Journal
14 (2007), no. 3, 389404. DVI PS PDF
[15] Further Combinatorial Identities Deriving from the nth
Power of a $2 \times 2$ Matrix (with Nancy Wyshinski)

Discrete Applied Mathematics 154
(2006), no. 8, 13011308.
DVI PS PDF
[20] Some more Long Continued Fractions, I (with Peter Zimmer)
 Acta Arith.127
(2007), no. 4, 365389.
DVI PS PDF
[21] Symmetry and specializability in the continued fraction
expansions of some infinite products
 The Journal of Number Theory127
(2007), no. 2, 184219. DVI PS PDF
[26] Some more identities of the RogersRamanujan type (with
Douglas Bowman and Andrew Sills)
 The
Ramanujan
Journal
Volume 18, Issue 3 (2009), Page
307 DVI PS PDF
[27] Some new Families of Tasoevian and Hurwitzian Continued
Fractions
 Acta
Arith.. 135 (2008), no. 3,
247268. DVI PS PDF
[30] RogersRamanujan Computer Searches (with Andrew Sills and
Peter Zimmer)
 Journal
of Symbolic Computation Volume 44, Issue 8,
August 2009, Pages 10681078 DVI PS PDF
[31] Lifting Bailey Pairs to WPBailey Pairs (with Andrew
Sills and Peter Zimmer)
 Discrete
Mathematics309 (2009), pp.
50775091 DVI PS PDF
[35] Continued Fraction Proofs of $m$versions of Some
Identities of RogersRamanujanSlater Type (with Doug Bowman and
Nancy Wyshinski)  The
Ramanujan Journal25,
Number 2, 203227 DVI PS PDF
[41] A HardyRamanujanRademachertype
formula for $(r,s)$regular partitions (with Scott Parsell)
 The
Ramanujan
Journal June 2012, Volume 28, Issue 2, pp 253271 DVI PS PDF
[42] On a pair of identities from Ramanujan's lost notebook
(with Andrew Sills)  Annals of Combinatorics
Volume 16, Number 3 (2012), 591607 DVI PS PDF
[43] A Reciprocity Relation for WPBailey Pairs (with Peter
Zimmer)  The
Ramanujan
Journal Volume 28, Number 2 (2012), 155173 DVI PS PDF
[44] Further results on vanishing coefficients in infinite product expansions  J. Aust. Math. Soc.98 (2015), no. 1, 69–77. DVI PS PDF
[45] General multisum transformations and some implications  The
Ramanujan
Journal April 2016, Volume 39, Issue 3, pp 545565 DVI PS PDF
[49] Mock Theta Function Identities Deriving from
Bilateral Basic Hypergeometric Series
 to appear in the refereed conference proceedings (to be published by Springer) of the
2016 Gainesville International Number Theory Conference in honour of Krishna Alladi. DVI PS PDF
[50] Asymptotics and Sequential Closures of Continued
Fractions
and Generalizations (with Douglas Bowman)
 submitted. DVI PS PDF