36 citations · 90 across the 10 of their papers we have counts for
5 papers · 1 filter
Arakelov class groups of random number fields
Alex Bartel, Henri Johnston, Hendrik W. Lenstra
The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen--Lenstra--Martinet he…
On class groups of random number fields
Alex Bartel, Hendrik W. Lenstra
The main aim of the present paper is to disprove the Cohen--Lenstra--Martinet heuristics in two different ways and to offer possible corrections. We also recast the heuristics in t…
Testing isomorphism of lattices over CM-orders
Hendrik W. Lenstra, Alice Silverberg
A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closel…
Lattices with Symmetry
H. W. Lenstra, A. Silverberg
For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a pr…
Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves
Manjul Bhargava, Daniel M. Kane, Hendrik W. Lenstra +2
Using maximal isotropic submodules in a quadratic module over Z_p, we prove the existence of a natural discrete probability distribution on the set of isomorphism classes of short…