Tommy Occhipinti

activity

20132015

most citedWhich finite simple groups are unit groups?

12 citations · 13 across the 3 of their papers we have counts for

collaborators

5 papers

math.NT2015

Wild ramification in a family of low-degree extensions arising from iteration

Benjamin Breen, Rafe Jones, Tommy Occhipinti +1

This article gives a first look at wild ramification in a family of iterated extensions. For integer values of c, we consider the splitting field of $(x^{2} + c)^{2} + c$ , the second i…

math.AG2014

Low-dimensional factors of superelliptic Jacobians

Thomas Occhipinti, Douglas Ulmer

Given a polynomial $f \in C [x]$ , we consider the family of superelliptic curves $y^{d} = f (x)$ and their Jacobians $J_{d}$ for varying integers $d$ . We show that for any integer $…

math.NT2014★ 1 cited

Explicit points on $y^{2} + x y - t^{d} y = x^{3}$ and related character sums

Christopher Davis, Tommy Occhipinti

Let $F_{q}$ denote a finite field of characteristic $p \geq 5$ and let $d = q + 1$ . Let $E_{d}$ denote the elliptic curve over the function field $F_{q^{2}} (t)$ defined b…

math.RA2014★ 12 cited

Which finite simple groups are unit groups?

Christopher Davis, Tommy Occhipinti

We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $…

math.RA2013

Which alternating and symmetric groups are unit groups?

Christopher Davis, Tommy Occhipinti

We prove there is no ring with unit group isomorphic to S_n for n \geq 5 and that there is no ring with unit group isomorphic to A_n for n \geq 5, n \neq 8. We give examples of rin…

Wild ramification in a family of low-degree extensions arising from iteration

Low-dimensional factors of superelliptic Jacobians

Explicit points on y2+xy−tdy=x3 and related character sums

Which finite simple groups are unit groups?

Which alternating and symmetric groups are unit groups?

Explicit points on $y^{2} + x y - t^{d} y = x^{3}$ and related character sums