3 papers
math.NT2026
Counting number fields of fixed degree by their smallest defining polynomial
Santiago Arango-Piñeros, Fabian Gundlach, Robert J. Lemke Oliver +5
When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of on the space of polynom…
math.NT2025
Malle's Conjecture for Galois octic fields over
Arul Shankar, Ila Varma
We compute the asymptotic number of octic number fields whose Galois groups over are isomorphic to , the symmetries of a square, when ordering such fields by their…
math.NT2024
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…