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Functional equations for Mahler measures of genus-one curves

- Matilde Lal'in, Mathew Rogers
- Mathematics
- 1 December 2006

In this paper we will establish functional equations for Mahler measures of families of genus-one two-variable polynomials. These families were previously studied by Beauville, and their Mahler… Expand

From L-series of elliptic curves to Mahler measures

- Mathew Rogers, W. Zudilin
- MathematicsCompositio Mathematica
- 14 December 2010

Abstract We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L-values of elliptic… Expand

Moments of elliptic integrals and critical $$L$$L-values

- Mathew Rogers, J. Wan, I. Zucker
- Mathematics
- 9 March 2013

We compute the critical $$L$$L-values of some weight 3, 4, or 5 modular forms, by transforming them into integrals of the complete elliptic integral $$K$$K. In doing so, we prove closed-form formulas… Expand

Spanning tree generating functions and Mahler measures

- A. Guttmann, Mathew Rogers
- Mathematics
- 12 July 2012

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when… Expand

On the Mahler Measure of 1+X+1/X+Y +1/Y

- Mathew Rogers, W. Zudilin
- Mathematics
- 6 February 2011

.The study of multi-variable Mahler measures originated in the work of Smyth, whoproved relations with Dirichlet L-values and special values of the Riemann zetafunction [22]. Formula (1) is the ﬁrst… Expand

New 5F4 hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π

- Mathew Rogers
- Mathematics
- 1 April 2009

Abstract
New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these… Expand

Hypergeometric Formulas for Lattice Sums and Mahler Measures

- Mathew Rogers
- Mathematics, PhysicsInternational Mathematics Research Notices
- 22 June 2008

Equation (3) is an interesting conjecture, because it relates a complicated lattice sum to the 3F2 hypergeometric function. Lattice sums have been extensively studied in physics, since they often… Expand

A SOLUTION OF SUN'S $520 CHALLENGE CONCERNING $\frac{520}{\pi}$

- Mathew Rogers, A. Straub
- Mathematics
- 8 October 2012

We prove a Ramanujan-type formula for 520/π conjectured by Zhi-Wei Sun. Our proof begins with a hypergeometric representation of the relevant double series, which relies on a recent generating… Expand

Secant zeta functions

- Matilde Lal'in, Francis Rodrigue, Mathew Rogers
- MathematicsJournal of Mathematical Analysis and Applications
- 14 April 2013

Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

- B. Berndt, George Lamb, Mathew Rogers
- Mathematics
- 25 August 2011

We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers–Ramanujan… Expand

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