M. Lalín

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20242026

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5 papers · 1 filter

math.NT2026

Machine learning the arithmetic of Boyd's Mahler measure conjectures

Alberto Alfarano, Pablo Bianucci, Matilde N. Lal\'Ä±n +1

Boyd conjectured that the Mahler measure of $P_{k} (x, y) = x + y + \frac{1}{x} + \frac{1}{y} + k$ for $k$ an integer, is given by $r_{k} L^{'} (E_{k}, 0)$ , where $E_{k}$ is the elliptic curve associated to…

math.NT2025

Nonvanishing of $L$ --functions associated to fixed order characters over function fields

Chantal David, Alexandra Florea, Matilde Lalin

We show that a positive proportion of the values $L (1/2, I ¨ _{c})$ are non-zero, where $I ¨ _{c}$ is the $ℓ^{th}$ residue symbol for $ℓ \geq 3$ over $F_{q} [t]$ , when av…

math.NT2025

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, $k$ -parameter family $x + y + k$ and prove explicit formulas that demonstrate its relation to the standard Mahler measure of thes…

math.NT2024

Moments of Artin-Schreier L-functions

Alexandra Florea, Edna Jones, Matilde Lalin

We compute moments of $L$ -functions associated to the polynomial family of Artin--Schreier covers over $F_{q}$ , where $q$ is a power of a prime $p > 2$ , when the size of the f…

math.NT2024

Asymmetric Distribution of Extreme Values of Cubic $L$ -functions at $s = 1$

Pranendu Darbar, Chantal David, Matilde Lalin +1

We investigate the distribution of values of cubic Dirichlet $L$ -functions at $s = 1$ . Following ideas of Granville and Soundararajan for quadratic $L$ -functions, we model the distri…