3 citations · 4 across the 13 of their papers we have counts for
14 papers · 1 filter
Beyond the unique pair: a two-parameter family of rational triangles with equal perimeter and area
Jesse Allen, Olivier Beaudry-Ogden, Théophane Bouchard +4
We study pairs consisting of a rational isosceles triangle and a rational triangle having a prescribed angle , with equal perimeter and equal area. Writing $ρ=\cos(θ)\in\mathbb{…
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…
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 fo…
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 varying even weight for any fixed congruence group and study the set of all of their zeros taken for a…
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…
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. Lalín, 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…
On the zeros of odd weight Eisenstein series
Jan-Willem van Ittersum, Berend Ringeling
We count the number of zeros of the holomorphic odd weight Eisenstein series in all -translates of the standard fundamental domain.
On the modulo zeros of modular forms congruent to theta series
Berend Ringeling
For a prime larger than , the Eisenstein series of weight has some remarkable congruence properties modulo . Those imply, for example, that the -invariants of it…
On Lehmer's question for integer-valued polynomials
Berend Ringeling
We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.
Critical points of modular forms
Jan-Willem van Ittersum, Berend Ringeling
We count the number of critical points of a modular form with real Fourier coefficients in a -translate of the standard fundamental domain (with $γ\in \mathrm{SL}_…
Exercising in complex Mahler measures: diamonds are not forever
Berend Ringeling, Wadim Zudilin
Recently, Hang Liu and Hourong Qin came up with a numerical observation about the relation between the Mahler measures of one hyperelliptic and two elliptic families. The discovere…
Hedgehogs in Lehmer's problem
Jan-Willem M. van Ittersum, Berend Ringeling, Wadim Zudilin
Motivated by a famous question of Lehmer about the Mahler measure we study and solve its analytic analogue.
Special zeta Mahler functions
Berend Ringeling
In 1969, I. Bernstein and S. Gelfand introduced an object, which is now called the zeta Mahler function (ZMF, also zeta Mahler measure) and related to the Mahler measure. Here we d…