Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants

By Manjul Bhargava. 2007

117 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/642098400058cc3b41bb55701051de50bd9dfcbf

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Citations in the corpus

On the Davenport–Heilbronn theorems and second order terms (2010, background): “Such “mass formulae” for local fields and orders in fact hold in far more generality (in particular, for degrees other than 3); see [6, 29], and [9].”
The density of discriminants of quartic rings and fields (2005, background): “For more details on the evaluation of local sums of the form (3), and for global heuristics on the expected values of the asymptotic constants associated to general degree n Sn-number fields, see [5].”
On the probabilities of local behaviors in abelian field extensions (2008, background): “For degree n extensions having Galois closure with Galois group Sn, it is known that when counting by discriminant for n = 2, 3, 4, and 5, local completions Lv show up with probability proportional to 1 |AutQv Lv| 1 |DiscLv| (see [11], [3], and [4] for the computation of the probabilities, and [5] f”
Heights on stacks and a generalized Batyrev–Manin–Malle conjecture (2021, background): “(The prediction of c is much more delicate: see Peyre [51, Définition 2.1] for the Batyrev–Manin case, and Bhargava [9] for the Malle case, in the special case G = Sn.”
The asymptotic growth of torsion homology for arithmetic groups (2010, methodology): “Bhargava’s heuristics.”
Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces (2015, unknown): “Then as N p → ∞ , µ τ ( p ) is bounded above by a constant c τ := 1 / #Aut( τ ) which is strictly between 0 and 1; this follows from [19, Lemma 18], [3, Lemma 21], [4, Lemma 20] (see [5] for the definition of #Aut( τ )).”