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20102020
most citedThe mean number of 2-torsion elements in the class groups of -monogenized cubic fields

4 citations · 7 across the 3 of their papers we have counts for

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math.NT2020★ 4 cited

The mean number of 2-torsion elements in the class groups of -monogenized cubic fields

Manjul Bhargava, Jonathan Hanke, Arul Shankar

We prove that, on average, the monogenicity or -monogenicity of a cubic field has an altering effect on the behavior of the 2-torsion in its class group.

math.NT2012

Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields

Jonathan Hanke

In this paper we describe an algorithm that quickly computes a maximal a-valued lattice in an F-vector space equipped with a non-degenerate bilinear form, where a is a fractional i…

math.NT2010★ 3 cited

A proof of the S-genus identities for ternary quadratic forms

Alexander Berkovich, Jonathan Hanke, William Jagy

In this paper we prove the main conjectures of Berkovich and Jagy about weighted averages of representation numbers over an S-genus of ternary lattices (defined below) for any odd…