6 papers
Machine learning the arithmetic of Boyd's Mahler measure conjectures
Alberto Alfarano, Pablo Bianucci, Matilde N. Lal\'ın +1
Boyd conjectured that the Mahler measure of for an integer, is given by , where is the elliptic curve associated to…
The asymptotic Mahler measure of Gaussian periods
Gunther Cornelissen, David Hokken, Berend Ringeling
We construct a sequence of cyclotomic integers (Gaussian periods) of particularly small Mahler measure/height. We study the asymptotics of their Mahler measure as a function of the…
Relating Mahler measures and Dirichlet -values: new evidence for Chinburg's conjectures
David Hokken, Mahya Mehrabdollahei, Berend Ringeling
Let be the odd quadratic Dirichlet character of conductor , and let denote the Mahler measure of a polynomial . In 1984, Chinburg conjectured that f…
Geodesic clustering of zeros of Eisenstein series for congruence groups
Sebastián Carrillo Santana, Gunther Cornelissen, Berend Ringeling
We consider a set of generators for the space of Eisenstein series of even weight for any congruence group and study the set of all of their zeros taken for -conjug…
On twisted period functions and Moments of a weighted mean square of Dirichlet L-functions on the critical line
Sebastien Darses, Berend Ringeling, Emmanuel Royer
We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties -- including Eisenstein series and period functions -- that were…
Random walks through the areal Mahler measure: steps in the complex plane
Matilde N. LalÃn, Siva Sankar Nair, Berend Ringeling +1
We study the areal Mahler measure of the two-variable, -parameter family and prove explicit formulas that demonstrate its relation to the standard Mahler measure of thes…