H. Helfgott

activity

19982025

most citedMinor arcs for Goldbach's problem

50 citations · 353 across the 37 of their papers we have counts for

collaborators

42 papers

math.NT2025

Optimal bounds for sums of non-negative arithmetic functions

Andrés Chirre, Harald Andrés Helfgott

Let $A (s) = \sum_{n} a_{n} n^{- s}$ be a Dirichlet series admitting meromorphic continuation to the complex plane. Assume we know the location of the poles of $A (s)$ with $|\Im s| \leq…

math.NT2025

Optimal bounds for sums of bounded arithmetic functions

Andrés Chirre, Harald Andrés Helfgott

Let $A (s) = \sum_{n} a_{n} n^{- s}$ be a Dirichlet series with meromorphic continuation. Say we are given information on the poles of $A (s)$ with $∣ℑ s ∣ \leq T$ for some large constan…

math.GR2023

New dimensional estimates for subvarieties of linear algebraic groups

Jitendra Bajpai, Daniele Dona, Harald Andrés Helfgott

For every connected, almost simple linear algebraic group $G \leq GL_{n}$ over a large enough field $K$ , every subvariety $V \subseteq G$ , and every finite generating set $A\…

math.NT2022★ 1 cited

Expansion, divisibility and parity: an explanation

Harald Andrés Helfgott

After seeing how questions on the finer distribution of prime factorization -- considered inaccessible until recently -- reduce to bounding the norm of an operator defined on a gra…

math.GR2021★ 2 cited

Growth estimates and diameter bounds for untwisted classical groups

Jitendra Bajpai, Daniele Dona, Harald Andrés Helfgott

Babai's conjecture states that, for any finite simple non-abelian group $G$ , the diameter of $G$ is bounded by $(lo g ∣ G ∣)^{C}$ for some absolute constant $C$ . We prove that, for an…

math.NT2021★ 3 cited

Expansion, divisibility and parity

Harald Andrés Helfgott, Maksym Radziwiłł

Let $P \subset [H_{0}, H]$ be a set of primes, where $lo g H_{0} \geq (lo g H)^{2/3 + ε}$ . Let $L = \sum_{p \in P} 1/ p$ . Let $N$ be such that $\log H \leq (\…