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Functional equations for Mahler measures of genus-one curves
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
From L-series of elliptic curves to Mahler measures
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
Moments of elliptic integrals and critical $$L$$L-values
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
Spanning tree generating functions and Mahler measures
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
On the Mahler Measure of 1+X+1/X+Y +1/Y
.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
New 5F4 hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π
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
Hypergeometric Formulas for Lattice Sums and Mahler Measures
  • Mathew Rogers
  • Mathematics, Physics
    International 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
A SOLUTION OF SUN'S $520 CHALLENGE CONCERNING $\frac{520}{\pi}$
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
Secant zeta functions
Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi
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
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