7 citations · 10 across the 6 of their papers we have counts for
6 papers
Root of the generic cubic as a power series in the discriminant
Jason Bland, Skip Garibaldi, Joel Rosenberg
An observation of J-P. Serre implies that the generic monic cubic polynomial, unique among generic monic polynomials of degree at least two, has a root that is a power series in th…
The longest and shortest roots of a real cubic
Jason Bland, Skip Garibaldi, Joel Rosenberg
There are many formulas in the literature providing roots of a real cubic that avoid some of the well-known pathologies of Cardano's formulas. Among these, we identify two that con…
A new family of exceptional polynomials in characteristic two
Robert M. Guralnick, Joel E. Rosenberg, Michael E. Zieve
We produce a new family of polynomials f(x) over fields K of characteristic 2 which are exceptional, in the sense that f(x)-f(y) has no absolutely irreducible factors in K[x,y] bes…
The probability that a random monic p-adic polynomial splits into linear factors
Joe Buhler, Daniel Goldstein, David Moews +1
Let n be a positive integer and let p be a prime. We calculate the probability that a random monic polynomial of degree n with coefficients in the ring Z_p of p-adic integers split…
Hessian quartic surfaces that are Kummer surfaces
Joel E. Rosenberg
In 1899, Hutchinson presented a way to obtain a three-parameter family of Hessians of cubic surfaces as blowups of Kummer surfaces. We show that this family consists of those Hessi…
Rational and Non-Rational Algebraic Varieties: Lectures of János Kollár
Karen E. Smith, Joel Rosenberg
This is a detailed write-up of Kollár's course at the EMS summer school in Algebraic Geometry in Eger, Hungary, August 1996. The topics include definitions and examples of rational…