Modular equations and lattice sums
Number Theory
2011-08-02 v2
Abstract
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 of conductor 17 elliptic curves.
Keywords
Cite
@article{arxiv.1001.4496,
title = {Modular equations and lattice sums},
author = {Mathew Rogers and Boonrod Yuttanan},
journal= {arXiv preprint arXiv:1001.4496},
year = {2011}
}
Comments
12 pages, Rewritten and updated