English

Regulator proofs for Boyd's identities on genus 2 curves

Number Theory 2018-12-24 v1

Abstract

We use the elliptic regulator to recover some identities between Mahler measures involving certain families of genus 2 curves that were conjectured by Boyd and proven by Bertin and Zudilin by differentiating the Mahler measures and using hypergeometric identities. Since our proofs involve the regulator, they yield light into the expected relation of each Mahler measure to special values of LL-functions of certain elliptic curves.

Keywords

Cite

@article{arxiv.1811.05189,
  title  = {Regulator proofs for Boyd's identities on genus 2 curves},
  author = {Matilde Lalín and Gang Wu},
  journal= {arXiv preprint arXiv:1811.05189},
  year   = {2018}
}