7 papers
Counting metacyclic fields
Maddie Allen, Justine Dell, Milad Fakhari +3
By a metacyclic field we mean the Galois closure of a pure field , , of odd prime degree . Let denote the c…
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…
Counting fields with a power saving error term
Sambhabi Bose, Kevin J. McGown, Ishan Panpaliya +2
Let denote the number of degree extensions of with Galois closure and . Malle's conjecture predicts an asymptotic of the form $N_d(G,X…
Polynomial densities and Heilbronn's criterion
Alexis Hibbler, Kevin J. McGown, Enrique Treviño
Heilbronn gave a sufficient condition for a number field with a totally ramified prime to fail to be norm-Euclidean. We say that Heilbronn's criterion applies to a polynomial i…
The average genus number for pure fields of prime degree
Sambhabi Bose, Kevin J. McGown, Ishan Panpaliya +2
Let be prime. Let be the collection of (isomorphism classes of) pure number fields of degree , ordered by the abs…
The determination of norm-Euclidean cyclic cubic fields
Gustav Kjærbye Bagger, Gustav Kjærbye Bagger, Andrew R. Booker +5
It is known on the Generalised Riemann Hypothesis that there are precisely cyclic cubic fields that are norm-Euclidean. Unconditionally, there is a gap between analytic estima…