Mahler Measure of Families of Polynomials Defining Genus 2 and 3 Curves

2021 ◽  
pp. 1-16
Author(s):  
Hang Liu ◽  
Qin Hourong
Keyword(s):  
Mahler Measure ◽  
Genus 2

Regulator proofs for Boyd’s identities on genus 2 curves

2019 ◽  
Vol 15 (05) ◽  
pp. 945-967
Author(s):  
Matilde Lalín ◽  
Gang Wu
Keyword(s):  
Elliptic Curves ◽  
Mahler Measure ◽  
Special Values ◽  
Genus 2 ◽  
Genus 2 Curves

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.

scholarly journals On the Mahler measure of a family of genus 2 curves

2016 ◽  
Vol 283 (3-4) ◽  
pp. 1185-1193 ◽  
Author(s):  
Marie José Bertin ◽  
Wadim Zudilin
Keyword(s):  
Mahler Measure ◽  
Genus 2 ◽  
Genus 2 Curves

scholarly journals Contact structures and reducible surgeries

2015 ◽  
Vol 152 (1) ◽  
pp. 152-186 ◽  
Author(s):  
Tye Lidman ◽  
Steven Sivek
Keyword(s):  
Contact Structures ◽  
Surgery Theory ◽  
Contact Topology ◽  
Exceptional Surgery ◽  
Genus 2 ◽  
Cabling Conjecture

We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus$g$must have slope$2g-1$, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.

scholarly journals Some Remarks on the Uniformizing Function in Genus 2

2005 ◽  
Vol 115 (1) ◽  
pp. 121-133 ◽  
Author(s):  
Peter Buser ◽  
Robert Silhol
Keyword(s):  
Genus 2
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