12 citations · 23 across the 9 of their papers we have counts for
6 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}'…
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…
Averages and moments associated to class numbers of imaginary quadratic fields
D. R. Heath-Brown, L. B. Pierce
For any odd prime , let denote the -part of the class number of the imaginary quadratic field . Nontrivial pointwise upper bounds ar…
Burgess bounds for short mixed character sums
D. R. Heath-Brown, L. B. Pierce
This paper proves nontrivial bounds for short mixed character sums by introducing estimates for Vinogradov's mean value theorem into a version of the Burgess method.
Simultaneous Integer Values of Pairs of Quadratic Forms
D. R. Heath-Brown, L. B. Pierce
We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent "almost all" pairs of integers that satisfy the necessary local conditions, pr…