Mathew Rogers, Boonrod Yuttanan
Published 2010-01-25, updated 2011-07-31Version 2
We highlight modular equations discovered by Somos and Ramanujan, and use them to prove new relations between lattice sums and hypergeometric functions. We also discuss progress towards solving Boyd's Mahler measure conjectures, and we conjecture a new formula for $L(E,2)$ of conductor 17 elliptic curves.
Comments: 12 pages, Rewritten and updated
$y$-coordinates of elliptic curves
Moments of the critical values of families of elliptic curves, with applications
$_3F_2$ hypergeometric series and periods of elliptic curves
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