Modular equations and lattice sums

Details Modular equations and lattice sums Modular equations and lattice sums

2010-01-25

arxiv.org/abs/1001.4496v2

Mathematics

Number Theory

12 pages, Rewritten and updated

Scientific paper

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.

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