Artane Siad

collaborators

5 papers

math.NT2026

Monogenicity and 2-torsion in the class group of number fields of odd degree

Artane Siad

We study the average $2$ -torsion in the class group of monogenised fields of odd degree. Bhargava--Hanke--Shankar have recently shown that for a fixed signature, the average number…

math.NT2026

The existence of infinitely many cubic fields with class group of exact 2-rank 1

Manjul Bhargava, Arul Shankar, Artane Siad +1

We show that infinitely many cubic fields have class group of 2-rank 1.

math.NT2025

Hecke reciprocity and class groups

Ari Shnidman, Artane Siad

We compute the average size of $Cl_{F} [2]$ in the family of cubic fields $F = Q (3 n)$ . Specifically, as $F$ varies over the subfamily of wildly (resp. tamel…

math.NT2025

Counting integral points on symmetric varieties with applications to arithmetic statistics

Arul Shankar, Artane Siad, Ashvin A. Swaminathan

In this article, we combine Bhargava's geometry-of-numbers methods with the dynamical point-counting methods of Eskin--McMullen and Benoist--Oh to develop a new technique for count…

math.NT2025

Entropy of Cohen-Lenstra measures: the $u$ -aspect

Artane Siad

Let $H (I^½_{CL}^{u})$ be the entropy of the Cohen-Lenstra measure on finite abelian $p$ -groups associated to an integral unit-rank $0 \leq u \in N$ . In th…

Monogenicity and 2-torsion in the class group of number fields of odd degree

The existence of infinitely many cubic fields with class group of exact 2-rank 1

Hecke reciprocity and class groups

Counting integral points on symmetric varieties with applications to arithmetic statistics

Entropy of Cohen-Lenstra measures: the u-aspect

Entropy of Cohen-Lenstra measures: the $u$ -aspect