18 citations · 29 across the 11 of their papers we have counts for
13 papers
Rough numbers between consecutive primes
Ayla Gafni, Terence Tao
Using a sieve-theoretic argument, we show that almost all gaps between consecutive primes contain a natural number whose least prime factor $p(m…
On the number of exceptional intervals to the prime number theorem in short intervals
Ayla Gafni, Terence Tao
For a fixed exponent , it is expected that we have the prime number theorem in short intervals as . From the rece…
Exponential sums weighted by additive functions
Ayla Gafni, Nicolas Robles
We introduce a general class of additive functions such that and prove a tight bound for exponential sums of the form where $f \in…
Improved bounds on number fields of small degree
Theresa C. Anderson, Ayla Gafni, Kevin Hughes +5
We study the number of degree number fields with discriminant bounded by . In this article, we improve an upper bound due to Schmidt on the number of such fields that was pr…
Uniform distribution and geometric incidence theory
A. Gafni, A. Iosevich, E. Wyman
A celebrated unit distance conjecture due to Erd\H os says that that the unit distances cannot arise more than times (for any ) among points in the Euclidean…
Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver +3
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert…