20 citations · 41 across the 11 of their papers we have counts for
14 papers
Locally imprimitive points on elliptic curves
Nathan Jones, Francesco Pappalardi, Peter Stevenhagen
Under GRH, any element in the multiplicative group of a number field that is globally primitive (i.e., not a perfect power in ) is a primitive root modulo a set of primes…
Cyclic reduction densities for elliptic curves
Francesco Campagna, Peter Stevenhagen
For an elliptic curve defined over a number field , the heuristic density of the set of primes of for which has cyclic reduction is given by an inclusion-exclusion s…
Redei reciprocity, governing fields, and negative Pell
Peter Stevenhagen
We discuss the origin, an improved definition and the key reciprocity property of the trilinear symbol introduced by Rédei in the study of 8-ranks of narrow class groups of quadrat…
Adelic point groups of elliptic curves
Athanasios Angelakis, Peter Stevenhagen
We show that for an elliptic curve E defined over a number field K, the group E(A) of points of E over the adele ring A of K is a topological group that can be analyzed in terms of…
Genus-2 curves and Jacobians with a given number of points
Reinier Bröker, Everett W. Howe, Kristin E. Lauter +1
We study the problem of efficiently constructing a curve C of genus 2 over a finite field F for which either the curve C itself or its Jacobian has a prescribed number N of F-ratio…
Computing higher rank primitive root densities
P. Moree, P. Stevenhagen
We extend the character sum method for the computation of densities in Artin primitive root problems developed by H. W. Lenstra and the authors to the situation of radical extensio…