English

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 L(E,2)L(E,2) 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

R2 v1 2026-06-21T14:39:11.198Z