TL;DR
This paper explores conjectural links between Mahler measures of three-variable polynomials and special values of L-functions associated with elliptic curves, supported by numerical evidence.
Contribution
It introduces a novel perspective connecting Mahler measures to hypergeometric periods of elliptic curves, proposing new conjectural evaluations.
Findings
Numerical evidence for conjectural evaluations of L-values
Identification of Mahler measures as hypergeometric periods
Insights into the relationship between Mahler measures and elliptic curve L-values
Abstract
We discuss some (conjectural) evaluations of -values attached to elliptic curves of conductors 15, 21, 24 and 32 as "hypergeometric periods". These numerical observations are motivated by the Mahler measures of three-variable polynomials.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Meromorphic and Entire Functions