9 citations · 31 across the 18 of their papers we have counts for
20 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…
CM elliptic curves and vertically entangled 2-adic groups
Nathan Jones
Consider the elliptic curve given by the Weierstrass equation , which has complex multiplication by the order of conductor inside . It…
On the acyclicity of reductions of elliptic curves modulo primes in arithmetic progressions
Nathan Jones, Sung Min Lee
Let be an elliptic curve defined over and, for a prime of good reduction for let denote the reduction of modulo . Inspired by an ellip…
Elliptic curves with missing Frobenius traces
Nathan Jones, Kevin Vissuet
Let be an elliptic curve defined over . In 1976, Lang and Trotter conjectured an asymptotic formula for the number of primes of good reducti…
Elliptic curves with non-abelian entanglements
Nathan Jones, Ken McMurdy
We consider the problem of classifying quadruples where is a number field, is an elliptic curve defined over and is a pair of relatively pri…
The Lang-Trotter Conjecture for products of non-CM elliptic curves
Hao Chen, Nathan Jones, Vlad Serban
Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over and by the subsequent generalization of Co…