Regulator proofs for Boyd’s identities on genus 2 curves-Reference-Cited by-同舟云学术

Regulator proofs for Boyd’s identities on genus 2 curves

Published:2019-05-28 Issue:05 Volume:15 Page:945-967
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Lalín Matilde¹,Wu Gang¹

Affiliation:

1. Département de Mathématiques et de Statistique, Université de Montréal, Pavillon André-Aisenstadt, CP 6128, succ. Centre-ville, Montréal, Québec, Canada, H3C 3J7, Canada

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 [Formula: see text]-functions of certain elliptic curves.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119500519

Reference10 articles.

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5. Mahler's Measure and Special Values of L-functions

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