23 citations · 24 across the 5 of their papers we have counts for
12 papers · 1 filter
Geometry-of-numbers methods over global fields II: Coregular representations
Manjul Bhargava, Arul Shankar, Xiaoheng Wang
We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ra…
Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces
Manjul Bhargava, Arul Shankar, Xiaoheng Wang
We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techn…
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…
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.
Finiteness theorems for some representations of
Fatemehzahra Janbazi, Arul Shankar
Let be an integer and let be a number field with ring of integers . We prove that the set of ternary -ic forms with coefficients in …
Secondary terms in the counting functions of quartic fields
Arul Shankar, Jacob Tsimerman
We prove that the smoothed counting function of the set of quartic fields, satisfying any finite set of local conditions, can be written as a linear combination of $X,X^{5/6}\log X…