11 citations · 19 across the 5 of their papers we have counts for
7 papers
A minimalist version of the circle method and Diophantine problems over thin sets
Kirsti D. Biggs, Julia Brandes
This paper studies the minimal conditions under which we can establish asymptotic formulae for Waring's problem and other additive problems that may be tackled by the circle method…
Reinforcing a Philosophy: A counting approach to square functions over local fields
Kirsti D. Biggs, Julia Brandes, Kevin Hughes
In this paper, we study square functions for extension operators over finite-type, planar curves endowed with the Euclidean arclength measure. We prove new results for curves of th…
Efficient congruencing in ellipsephic sets: the general case
Kirsti D. Biggs
In this paper, we bound the number of solutions to a general Vinogradov system of equations , , as well as other related syste…
Efficient congruencing in ellipsephic sets: the quadratic case
Kirsti D. Biggs
In this paper, we bound the number of solutions to a quadratic Vinogradov system of equations in which the variables are required to satisfy digital restrictions in a given base. C…
Almost equal summands in Waring's problem with shifts
Kirsti Biggs
A result of Wright from 1937 shows that there are arbitrarily large natural numbers which cannot be represented as sums of th powers of natural numbers which are constrained…
Lower Bounds for Heights in Relative Galois Extensions
Shabnam Akhtari, Kevser Aktaş, Kirsti Biggs +3
The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our fir…