Ram Research Directory

James (MATH) McLaughlin

Education

• PhD, University of Illinois at Urbana-Champaign, 2002
• MSc, University College, Dublin, Ireland, 1996

Research Interests

integer partitionsbasic hypergeometric seriespolynomial continued fractionsDiophantine equations

Opportunities

Work Study Positions Available: No

Grant Funded Positions Available: No

Course-Credit Research Opportunities Available: No

Volunteer Research Positions Available: No

Contact Information

Phone: 610-430-4417

List of Publications

• Polynomial Continued Fractions (With D. Bowman) - Acta Arith. 103 (2002), no. 4, 329--342 On the Divergence of the Rogers-Ramanujan Continued Fraction on the Unit Circle (With D. Bowman) - The Transactions of the American Mathematical Society 356 (2004), no. 8, 3325--3347. Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields - J. London Math. Soc. (2) 67 (2003), no. 1, 16--28. Multi-variable Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields - Pacific J. Math. 210 (2003), no. 2, 335--349 On The Divergence in the General Sense of $q$-Continued Fractions on the Unit Circle (With D. Bowman) - Communications in the Analytic Theory of Continued Fractions 11(2003), 25--49. A Theorem on Divergence in the General Sense for Continued Fractions (With D. Bowman) - The Journal of Computational and Applied Mathematics 172, (2004) no. 2, pp 363--373. Real Numbers with Polynomial Continued Fraction Expansions (with Nancy Wyshinski) - Acta Arith. 116 (2005), no. 1, 63-79. Combinatorial Identities Deriving from the n-th Power of a $2 \times 2$ Matrix - INTEGERS: The Electronic Journal of Combinatorial Number Theory 4 (2004), A19, 14 pp. 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 1--2, 1 July 2005, Pages 255-262, containing the proceedings from the Conference on Orthogonal Functions and Related Topics, Roros, Norway, August 2003 Ramanujan and the Regular Continued Fraction Expansion of Real Numbers (with Nancy Wyshinski) - The Mathematical Proceedings of the Cambridge Philosophical Society, Volume 138 - Issue 03 - May 2005, pp 367 - 381. Powers of a matrix and combinatorial identities (with B. Sury) - INTEGERS: The Electronic Journal of Combinatorial Number Theory 5 (2005), A13, 9 pp. The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle (With D. Bowman) - The Rocky Mountain Journal of Mathematics 36 (2006), no. 3, 799--809. The Convergence behavior of $q$-Continued Fractions on the Unit Circle (With D. Bowman) - The Ramanujan Journal 12 (2006), no. 2, 185--195. Ramanujan and Extensions and Contractions of Continued Fractions (with Nancy Wyshinski) - The Ramanujan Journal 14 (2007), no. 3, 389--404. 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. Continued Fractions with Multiple Limits (With D. Bowman) - Advances In Mathematics Volume 210 (2007), no. 2, 578-606. A $q$-continued fraction (with Doug Bowman and Nancy Wyshinski) - International Journal of Number Theory Volume 2 (2006), no. 4, 523-547. Continued Fractions and Generalizations with Many Limits: A Survey. (with Doug Bowman) - In the Proceedings of the Conference on Diophantine Analysis and Related Fields, Keio University, Yokohama, JAPAN, 7-10 March, 2006 , published as Seminar on Mathematical Sciences, 35, Keio University, Department of Mathematics, Yokohama (2006), 19-38. Some properties of the distribution of the numbers of points on elliptic curves over a finite prime field (with Saiying He) - Bulletin of the Australian Mathematics Society 75 (2007), no. 1, 135--149. Some more Long Continued Fractions, I (with Peter Zimmer) - Acta Arith.127 (2007), no. 4, 365--389

Links

• ResearchGate