45 citations · 246 across the 34 of their papers we have counts for
4 papers · 1 filter
Remarks on the disproof of the unit distance conjecture
Noga Alon, Thomas F. Bloom, W. T. Gowers +6
We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdős unit distance conjecture, and a sequence of reflections on it. The a…
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…
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.