Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces

By Manjul Bhargava, A. Shankar, Xiaoheng Wang. 2015

68 citations recorded by the source corpus.

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 techniques to determine, for any base global field $F$ of characteristic not 2, the density of discriminants of field extensions of degree at most 5 over $F$.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3bccd349abc5a63ffcbd911be8bc18fe3a603e07

How researchers see this paper

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In Geometry and Topology

1. Melanie Matchett Wood
2. Caroline Turnage-Butterbaugh
3. L. Pierce
4. Dan Erik Petersen

In Mathematical Physics

1. Caroline Turnage-Butterbaugh
2. L. Pierce
3. Melanie Matchett Wood
4. Andr'as M'esz'aros
5. Hoi H. Nguyen
6. Dan Erik Petersen

Citations in the corpus

• An effective Chebotarev density theorem for families of number fields, with an application to $$\ell $$-torsion in class groups (2017, background): “Malle’s conjecture is known for quartic S4-fields due to Bhargava [Bha05] (over Q, in asymptotic form) and Bhargava, Shankar, and Wang [BSW15] (over global fields k, in asymptotic form).”