4 papers
math.NT2020
Non-monogenic Division Fields of Elliptic Curves
Hanson Smith
For various positive integers , we show the existence of infinite families of elliptic curves over with -division fields, , that are not monoge…
math.NT2020
A Divisor Formula and a Bound on the -gonality of the Modular Curve
Mark van Hoeij, Hanson Smith
We give a formula for divisors of modular units on and use it to prove that the -gonality of the modular curve is bounded above by $\left[\frac{11N^2}…
math.NT2019
The Monogeneity of Kummer Extensions and Radical Extensions
Hanson Smith
We give necessary and sufficient conditions for the Kummer extension to be monogenic over with as a generato…
math.NT2017
A family of monogenic quartic fields arising from elliptic curves
T. Alden Gassert, Hanson Smith, Katherine E. Stange
We consider partial torsion fields (fields generated by a root of a division polynomial) for elliptic curves. By analysing the reduction properties of elliptic curves, and applying…