11 citations · 12 across the 8 of their papers we have counts for
7 papers · 1 filter
On the Geometry and Shapes of Rank 2 Log Unit Lattices
Jose Cruz, Erik Holmes, Fatemeh Jalalvand +3
Every number field canonically gives rise to two lattices: its ring of integers and its log unit lattice. While the shapes of the former have undergone extensive research, far less…
Orientations and cycles in supersingular isogeny graphs
Sarah Arpin, Mingjie Chen, Kristin E. Lauter +3
The paper concerns several theoretical aspects of oriented supersingular -isogeny volcanoes and their relationship to closed walks in the supersingular -isogeny graph.…
Orienteering with one endomorphism
Sarah Arpin, Mingjie Chen, Kristin E. Lauter +3
In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is…
Class number and regulator computation in cubic function fields
Eric Landquist, Renate Scheidler, Andreas Stein
We present computational results on the divisor class number and the regulator of a cubic function field over a large base field. The underlying method is based on approximations o…
Tabulation of cubic function fields via polynomial binary cubic forms
Pieter Rozenhart, Michael Jacobson, Renate Scheidler
We present a method for tabulating all cubic function fields over whose discriminant has either odd degree or even degree and the leading coefficient of …
Computing quadratic function fields with high 3-rank via cubic field tabulation
Pieter Rozenhart, Michael Jacobson, Renate Scheidler
This paper presents an algorithm for generating all imaginary and unusual discriminants up to a fixed degree bound that define a quadratic function field of positive 3-rank. Our me…
Class Number and Regulator Computation in Purely Cubic Function Fields of Unit Rank Two
Felix Fontein, Eric Landquist, Renate Scheidler
We describe and give computational results of a procedure to compute the divisor class number and regulator of most purely cubic function fields of unit rank 2. Our implementation…