7 papers · 1 filter
Genuine and strongly genuine polynomials: With an application to the persistence of Galois groups under specialization
Dante Bonolis, Lillian B. Pierce, Katharine Woo
We develop the theory of strongly -genuine polynomials , which have the property that the number of specializations with $\mathbf{x}'…
The distribution of prime values of random polynomials
Noah Kravitz, Katharine Woo, Max Wenqiang Xu
The Bateman--Horn Conjecture predicts how often an irreducible polynomial assumes prime values. We demonstrate that with sufficient averaging in the coeffi…
Counting points on a family of degree one del Pezzo surfaces
Katharine Woo
We study rational points on the elliptic surface given by the equation: where satisfy that and $Q(u,v…
Stratification theorems for exponential sums in families
Dante Bonolis, Emmanuel Kowalski, Katharine Woo
We survey some of the stratification theorems concerning exponential sums over finite fields, especially those due to Katz-Laumon and Fouvry-Katz, as well as some of their applicat…
Counting integral points in thin sets of type II: singularities, sieves, and stratification
Dante Bonolis, Lillian B. Pierce, Katharine Woo
Consider an absolutely irreducible polynomial that is monic in and is a polynomial in for an integer . Le…
On Manin's conjecture for Châtelet surfaces
Katharine Woo
We resolve Manin's conjecture for all Châtelet surfaces over .
Prime Number Theorems for Polynomials from Homogeneous Dynamics
Giorgos Kotsovolis, Katharine Woo
We establish a new class of examples of the multivariate Bateman-Horn conjecture by using tools from dynamics. These cases include the determinant polynomial on the space of $n\tim…