4 papers
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}'…
A guide to Tauberian theorems for arithmetic applications
Lillian B. Pierce, Caroline L. Turnage-Butterbaugh, Asif Zaman
A Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theo…
Counting points in thin sets: A survey
Dante Bonolis, Lillian B. Pierce, Katharine Woo
In the 1980's Serre asked how many points of bounded height can lie in a thin set. This has motivated significant research ever since, culminating in a series of recent breakthroug…
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…