K. Woo

collaborators

5 papers

math.NT2026

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 $n$ -genuine polynomials $F (Y, X_{1}, \dots, X_{n})$ , which have the property that the number of specializations $F (Y, X_{1}, x^{'})$ with $\mathbf{x}'…

math.NT2026

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…

math.NT2026

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: $y^{2} = x^{3} + A x Q (u, v)^{2} + B Q (u, v)^{3},$ where $A, B \in Z$ satisfy that $4 A^{3} - 27 B^{2} \neq = 0$ and $Q(u,v…

math.NT2025

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 $f (x) \in Z [x]$ assumes prime values. We demonstrate that with sufficient averaging in the coeffi…

math.NT2025

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 $F (Y, X_{1}, \dots, X_{n}) \in Z [Y, X_{1}, \dots, X_{n}]$ that is monic in $Y$ and is a polynomial in $Y^{m}$ for an integer $m \geq 1$ . Le…