Terence Tao

activity

20242026

most citedLocal Bernstein theory, and lower bounds for Lebesgue constants

1 citations · 1 across the 3 of their papers we have counts for

collaborators

7 papers

math.NT2026

Products of consecutive integers with unusual anatomy

Terence Tao

Call an interval ${N + 1, \dots, N + H}$ of consecutive natural numbers \emph{bad} if the product $(N + 1) \dots (N + H)$ is divisible by the square of its largest prime factor; \emph{very…

math.CA2026★ 1 cited

Local Bernstein theory, and lower bounds for Lebesgue constants

Terence Tao

Classical (or ``global'') Bernstein theory establishes sharp control on entire functions of exponential type that are bounded and real-valued on the real axis. We localize some of…

math.NT2025

Quantitative correlations and some problems on prime factors of consecutive integers

Terence Tao, Joni Teräväinen

We consider several old problems involving the number of prime divisors function $ω (n)$ , as well as the related functions $Ω (n)$ and $τ (n)$ . Firstly, we show that there are infinit…

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

Decomposing a factorial into large factors

Boris Alexeev, Evan Conway, Matthieu Rosenfeld +4

Let $t (N)$ denote the largest number such that $N!$ can be expressed as the product of $N$ integers greater than or equal to $t (N)$ . The bound $t (N) / N = 1/ e - o (1)$ was apparently es…

math.NT2024

Higher uniformity of arithmetic functions in short intervals II. Almost all intervals

Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao +2

We study higher uniformity properties of the von Mangoldt function $Λ$ , the Möbius function $μ$ , and the divisor functions $d_{k}$ on short intervals $(x, x + H]$ for almost all $x \in…