A. Gafni

activity

20092025

most citedAdditive energy and the metric Poissonian property

18 citations · 29 across the 11 of their papers we have counts for

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3 papers · 1 filter

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

math.NT2025

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 $\sum_{n \leq x} f (n) e (α n)$ where $f \in…