36 citations · 71 across the 10 of their papers we have counts for
15 papers
Murmurations of quadratic and cubic characters over function fields
Matilde Lalín, Kyu-Hwan Lee, Thomas Oliver +1
We compute the murmuration density for the family of quadratic characters over function fields. We show that the expectation of this density coincides with a correction term arisin…
Dynamical Mahler Measure: A survey and some recent results
Annie Carter, Matilde Lalín, Michelle Manes +1
We study the dynamical Mahler measure of multivariate polynomials and present dynamical analogues of various results from the classical Mahler measure as well as examples of formul…
On the Northcott property of zeta functions over function fields
Xavier Généreux, Matilde Lalín, Wanlin Li
Pazuki and Pengo defined a Northcott property for special values of zeta functions of number fields and certain motivic -functions. We determine the values for which the Northco…
Spherical Heron triangles and elliptic curves
Tinghao Huang, Matilde Lalín, Olivier Mila
We define spherical Heron triangles (spherical triangles with "rational" side-lengths and angles) and parametrize them via rational points of certain families of elliptic curves. W…
Two-variable polynomials with dynamical Mahler measure zero
Annie Carter, Matilde Lalín, Michelle Manes +2
We discuss several aspects of the dynamical Mahler measure for multivariate polynomials. We prove a weak dynamical version of Boyd--Lawton formula and we characterize the polynomia…
Sums of divisor functions and von Mangoldt convolutions in leading to symplectic distributions
Vivian Kuperberg, Matilde Lalín
In [arXiv:1504.07804], Keating, Rodgers, Roditty-Gershon and Rudnick established relationships of the mean-square of sums of the divisor function over short intervals and…
Hyperbolic Heron Triangles and Elliptic Curves
Matilde Lalín, Olivier Mila
We define hyperbolic Heron triangles (hyperbolic triangles with "rational" side-lengths and area) and parametrize them in two ways as rational points of certain elliptic curves. We…
Counting Salem numbers of arithmetic hyperbolic 3-orbifolds
Mikhail Belolipetsky, Matilde Lalín, Plinio G. P. Murillo +1
It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon. We show tha…
Regulator proofs for Boyd's identities on genus 2 curves
Matilde Lalín, Gang Wu
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…
Mahler Measure and the Vol-Det Conjecture
Abhijit Champanerkar, Ilya Kofman, Matilde Lalín
The Vol-Det Conjecture relates the volume and the determinant of a hyperbolic alternating link in . We use exact computations of Mahler measures of two-variable polynomials to…
The distribution of -points on cyclic -covers of genus
Alina Bucur, Chantal David, Brooke Feigon +4
We study fluctuations in the number of points of -cyclic covers of the projective line over the finite field when is fixed and the genus…
Secant Zeta Functions
Matilde Lalín, Francis Rodrigue, Mathew Rogers
We study the series , and prove that it converges under mild restrictions on and . The function possesses a modular transformati…
A generalization of a theorem of Boyd and Lawton
Zahraa Issa, Matilde Lalín
The Mahler measure of a nonzero -variable polynomial is the integral of on the unit -torus. A result of Boyd and Lawton says that the Mahler measure of a multiv…
The fluctuations in the number of points of smooth plane curves over finite fields
Alina Bucur, Chantal David, Brooke Feigon +1
In this note, we study the fluctuations in the number of points of smooth projective plane curves over finite fields as is fixed and the genus varies. More preci…
Statistics for traces of cyclic trigonal curves over finite fields
Alina Bucur, Chantal David, Brooke Feigon +1
We study the variation of the trace of the Frobenius endomorphism associated to a cyclic trigonal curve of genus g over a field of q elements as the curve varies in an irreducible…