Mathew Rogers University of Montreal Department of Mathematics mdrogers [at] dms [dot] umontreal [dot] ca

Research:

My research area is analytic number theory and classical analysis.  I am interested in problems relating to Mahler measures,
hypergeometric functions, the Bloch-Beilinson conjectures, and lattice sums.

Research Statement.

CV.

Publications:

12. Variations of the Ramanujan polynomials and remarks on $\zeta(2j+1)/\pi^{2j+1}$,
        with M. N. Lalin, to appear in Functiones et Approximatio Commentarii Math.

11. Two-dimensional series evaluations via Ramanujan's elliptic functions,
        with B. C. Berndt and G. Lamb, to appear in the Ramanujan Journal.

10. On the Mahler measure of $1+X+1/X+Y+1/Y$,
        with W. Zudilin, Submitted.

9. From $L$-series of elliptic curves to Mahler measures,
        with W. Zudilin, Compositio Mathematica 148 (2012), no. 2, 385-414.

8. Mahler measure and the WZ algorithm,
        with J. Guillera, Submitted.

7. Modular equations and lattice sums,
        with B. Yuttunan, to appear in Computational and Analytical Mathematics, Springer Proceedings in Mathematics, (refereed).

6. Hypergeometric formulas for lattice sums and Mahler measures,
        International Mathematics Research Notices (2011), no. 17, 4027-4058.

4. New $_5F_4$ hypergeometric transformations, three-variable Mahler measures, and formulas for $1/\pi$,
        Ramanujan Journal 18 (2009), no. 3, 327--340.

3. Functional equations for Mahler measures of genus-one curves,
        with M. N. Lalin, Algebra and Number Theory 1 (2007), no. 1, 87-117.

2. 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.

1. Partial fractions expansions and identities for products of Bessel functions,
        Journal of Mathematical Physics 46 (2005), 18 pages.

Problems and Solutions: