1 citations · 2 across the 7 of their papers we have counts for
7 papers
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.
Hecke reciprocity and class groups
Ari Shnidman, Artane Siad
We compute the average size of in the family of cubic fields . Specifically, as varies over the subfamily of wildly (resp. tamel…
Entropy of Cohen-Lenstra measures: the -aspect
Artane Siad
Let be the entropy of the Cohen-Lenstra measure on finite abelian -groups associated to an integral unit-rank . In thi…
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…
Geometry-of-numbers methods in the cusp
Arul Shankar, Artane Siad, Ashvin Swaminathan +1
In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We il…
Monogenic fields with odd class number Part II: even degree
Artane Siad
In 1801, Gauss proved that there were infinitely many quadratic fields with odd class number. We generalise this result by showing that there are infinitely many -fields of an…
Monogenicity and 2-torsion in the class group of number fields of odd degree
Artane Siad
We study the average -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…