Regulators of Siegel units and applications
Fran\c{c}ois Brunault
TL;DR
This paper derives a formula for the regulator of Siegel units using L-values of Eisenstein series and applies it to conjectures related to elliptic curves with specific conductors.
Contribution
It introduces a new explicit formula connecting Siegel units regulators with L-values of Eisenstein series and demonstrates applications to notable elliptic curve conjectures.
Findings
Formula for regulator of Siegel units in terms of L-values
Applications to Boyd's and Zagier's conjectures for specific elliptic curves
Insights into elliptic curves of conductors 14, 21, 35, 48, and 54
Abstract
We present a formula for the regulator of two arbitrary Siegel units in terms of L-values of pairwise products of Eisenstein series of weight one. We give applications to Boyd's conjectures and Zagier's conjectures for elliptic curves of conductor 14, 21, 35, 48 and 54.
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