1 citations · 1 across the 1 of their papers we have counts for
4 papers
The shapes of Galois quartic fields
Piper H, Robert Harron
We determine the shapes of all degree number fields that are Galois. These lie in four infinite families depending on the Galois group and the tame versus wild ramification of…
Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent
Robert Harron
We show that the shape of a complex cubic field lies on the geodesic of the modular surface defined by the field's trace-zero form. We also prove a general such statement for all o…
Explicit computations of Hida families via overconvergent modular symbols
Evan P. Dummit, Márton Hablicsek, Robert Harron +3
In [Pollack-Stevens 2011], efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of -adic -funct…
The shapes of pure cubic fields
Robert Harron
We determine the shapes of pure cubic fields and show that they fall into two families based on whether the field is wildly or tamely ramified (of Type I or Type II in the sense of…