T. Tao

activity

19972023

most citedRandom matrices: Universality of local eigenvalue statistics up to the edge

276 citations · 4.5k across the 293 of their papers we have counts for

collaborators

Showing 2015 · math.NTShow all

4 papers · 2 filters

math.NT2015

Chains of large gaps between primes

Kevin Ford, James Maynard, Terence Tao

Let $p_{n}$ denote the $n$ -th prime, and for any $k \geq 1$ and sufficiently large $X$ , define the quantity $$ G_k(X) := \max_{p_{n+k} \leq X} \min( p_{n+1}-p_n, \dots, p_{n+k}-p_{n+…

math.NT2015★ 9 cited

Sign patterns of the Liouville and Möbius functions

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

Let $λ$ and $μ$ denote the Liouville and Möbius functions respectively. Hildebrand showed that all eight possible sign patterns for $(λ (n), λ (n + 1), λ (n + 2))$ occur infinitely often.…

math.NT2015★ 13 cited

The logarithmically averaged Chowla and Elliott conjectures for two-point correlations

Terence Tao

Let $λ$ denote the Liouville function. The Chowla conjecture, in the two-point correlation case, asserts that $n \leq x \sum λ (a_{1} n + b_{1}) λ (a_{2} n + b_{2}) = o (x)$ as $x \to \in…

math.NT2015★ 132 cited

An averaged form of Chowla's conjecture

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao

Let $λ$ denote the Liouville function. A well known conjecture of Chowla asserts that for any distinct natural numbers $h_{1}, \dots, h_{k}$ , one has $\sum_{1 \leq n \leq X} λ(n+h_1) \do…