- Title
- Further explorations of Boyd's conjectures and a conductor 21 elliptic curve
- Creator
- Lalín, Matilde; Samart, Detchat; Zudilin, Wadim
- Relation
- ARC.DP140101186 http://purl.org/au-research/grants/arc/DP140101186
- Relation
- Journal of the London Mathematical Society Vol. 93, Issue 2, p. 341-360
- Publisher Link
- http://dx.doi.org/10.1112/jlms/jdv073
- Publisher
- Oxford University Press
- Resource Type
- journal article
- Date
- 2016
- Description
- We prove that the (logarithmic) Mahler measure m(P) of P(x,y)=x+1/x+y+1/y+3 is equal to the L-value 2L'(E,0) attached to the elliptic curve E:P(x,y)=0 of conductor 21. In order to do this, we investigate the measure of a more general Laurent polynomial: Pa,b,c(x,y)=a(x+1/x)+b(y+1/y)+c] and show that the wanted quantity m(P) is related to a 'half-Mahler' measure of P(x,y)=P √7,1,3(x,y). In the finale, we use the modular parametrization of the elliptic curve P(x,y)=0, again of conductor 21, due to Ramanujan and the Mellit-Brunault formula for the regulator of modular units.
- Subject
- Mahler measure; Laurent polynomials; Boyd’s conjectures
- Identifier
- http://hdl.handle.net/1959.13/1324180
- Identifier
- uon:24975
- Identifier
- ISSN:0024-6107
- Rights
- This is the accepted version of the following article: Lalin, Matilde; Samart, Detchat; Zudilin, Wadim. "Further explorations of Boyd's conjectures and a conductor 21 elliptic curve" published in Journal of the London Mathematical Society, (2016) which has been published in final form at http://dx.doi.org/10.1112/jlms/jdv073
- Language
- eng
- Full Text
- Reviewed
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