4 citations · 11 across the 9 of their papers we have counts for
11 papers · 1 filter
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…
Iwasawa theory for symmetric powers of CM modular forms at nonordinary primes, II
Robert Harron, Jonathan Pottharst
Continuing the study of the Iwasawa theory of symmetric powers of CM modular forms at supersingular primes begun by the first author and Antonio Lei, we prove a Main Conjecture equ…
Counting elliptic curves with prescribed torsion
Robert Harron, Andrew Snowden
Mazur's theorem states that there are exactly 15 possibilities for the torsion subgroup of an elliptic curve over the rational numbers. We determine how often each of these groups…
On symmetric power L-invariants of Iwahori level Hilbert modular forms
Robert Harron, Andrei Jorza
We compute the arithmetic L-invariants (of Greenberg-Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under s…
Gauss-Manin connections for p-adic families of nearly overconvergent modular forms
Robert Harron, Liang Xiao
We interpolate the Gauss-Manin connection in p-adic families of nearly overconvergent modular forms. This gives a family of Maass-Shimura type differential operators from the space…
Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes
Robert Harron, Antonio Lei
Let f be a cuspidal newform with complex multiplication (CM) and let p be an odd prime at which f is non-ordinary. We construct admissible p-adic L-functions for the symmetric powe…
The exceptional zero conjecture for symmetric powers of CM modular forms: the ordinary case
Robert Harron
We prove the exceptional zero conjecture for the symmetric powers of CM cuspidal eigenforms at ordinary primes. In other words, we determine the trivial zeroes of the associated p-…
On Greenberg's -invariant of the symmetric sixth power of an ordinary cusp form
Robert Harron
We derive a formula for Greenberg's -invariant of Tate twists of the symmetric sixth power of an ordinary non-CM cuspidal newform of weight , under some technical assumpt…