Nancy and I also organized special sessions on continued fractions
at the 2006 Joint Meetings in San Antonio and 2004 Joint Meetings in Phoenix.
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 main areas of interest are in Number Theory.
I am currently working on various problems related to continued fractions.
Some of this work concerns the problem of finding polynomial solutions to
Pell's equation (thereby being able to write down expressions for the
fundamental unit in infinite families of real quadratic fields).
I have also investigated various convergence problems for q-continued
fractions, and I and my thesis adviser,
Douglas Bowman,
recently partially settled a long-standing open problem on the convergence
of the Rogers-Ramanujan 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.
Fall 2005 - Math 121 (Statistics), Math 151 (Introduction to Discrete Mathematics), Math 411 (Algebra I).
Spring 2006 - Math 105 (College Algebra), Math 151 (Introduction to Discrete Mathematics), Math 414 (Number Theory).
Fall 2006 - Math 121 (Statistics), Math 151 (Introduction to Discrete Mathematics), Math 411 (Algebra I).
Spring 2007 - Math 105 (College Algebra), Math 151 (Introduction to Discrete Mathematics), Math 121 (Statistics).
Fall 2007 - Math 105 (College Algebra), Math 411 (Algebra I).
Spring 2008 - Math 105 (College Algebra), Math 405 (q-series), Math 414 (Number Theory).
Students can access course information through
Blackboard .
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, 329--342.
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, 16--28.
DVI
PS
PDF
[4] Multi-variable Polynomial Solutions to Pell's Equation and Fundamental
Units in Real Quadratic Fields
-
Pacific J. Math.210 (2003),
no. 2, 335--349.
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, 185--195.
DVI
PS
PDF
[14] Ramanujan and Extensions and Contractions of Continued Fractions (with Nancy Wyshinski)
- The Ramanujan Journal
14 (2007),
no. 3, 389--404.
DVI
PS
PDF
[15] Further Combinatorial Identities Deriving from the n-th Power of a $2 \times 2$ Matrix
(with Nancy Wyshinski) - Discrete Applied Mathematics
154 (2006),
no. 8, 1301--1308.
DVI
PS
PDF
[20] Some more Long Continued Fractions, I (with Peter Zimmer)
-
Acta Arith.127 (2007),
no. 4, 365--389.
DVI
PS
PDF
[21] Symmetry and specializability in the continued fraction expansions of
some infinite products
- The Journal of Number Theory127 (2007),
no. 2, 184--219.
DVI
PS
PDF
[26] Some more identities of the Rogers-Ramanujan 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, 247--268.
DVI
PS
PDF
[31] Lifting Bailey Pairs to WP-Bailey Pairs (with Andrew Sills and Peter Zimmer)
-
Discrete Mathematics309 (2009), pp. 5077-5091
DVI
PS
PDF
[32] Asymptotics and Sequential Closures of Continued Fractions and Generalizations (with Douglas Bowman)
- submitted.
DVI
PS
PDF
[33] An Identity Motivated by an Amazing Identity of Ramanujan
- submitted.
DVI
PS
PDF
[34] Some Applications of a
Bailey-type Transformation (with Peter Zimmer)
- Submitted
DVI
PS
PDF
[35] General WP-Bailey Chains (with Peter Zimmer)
- submitted.
DVI
PS
PDF
[36] Some implications of Chu's $_{10}\psi_{10}$
extension of Bailey's $_{6}\psi_{6}$ summation formula (with Andrew Sills and Peter Zimmer)
- submitted.
DVI
PS
PDF
[37] Some new Transformations for Bailey pairs and WP-Bailey Pairs
- submitted.
DVI
PS
PDF
[38] Some Further Transformations for WP-Bailey Pairs
- submitted.
DVI
PS
PDF
[39] New Summation Formulae for some $q$-products - submitted.
DVI
PS
PDF
