A. Gafni

activity

20242026

collaborators

4 papers

math.NT2026

Exponential sums weighted by additive functions

Ayla Gafni, Nicolas Robles

We introduce a general class $F_{0}$ of additive functions $f$ such that $f (p) = 1$ and prove a tight bound for exponential sums of the form $\sum_{n \leq x} f (n) e (I^\pm n)$ where $f \in…

math.NT2025

Rough numbers between consecutive primes

Ayla Gafni, Terence Tao

Using a sieve-theoretic argument, we show that almost all gaps $(p_{n}, p_{n + 1})$ between consecutive primes $p_{n}, p_{n + 1}$ contain a natural number $m$ whose least prime factor $p(m…

math.NT2025

On the number of exceptional intervals to the prime number theorem in short intervals

Ayla Gafni, Terence Tao

For a fixed exponent $0 < I^¸ \leq 1$ , it is expected that we have the prime number theorem in short intervals $\sum_{x \leq n < x + x^{I^} ¸} I^ (n) \sim x^{I^} ¸$ as $x \to \infty$ . From the…

math.NT2024

Improved bounds on number fields of small degree

Theresa C. Anderson, Ayla Gafni, Kevin Hughes +5

We study the number of degree $n$ number fields with discriminant bounded by $X$ . In this article, we improve an upper bound due to Schmidt on the number of such fields that was pr…