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

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Showing 2014 · math.NTShow all

4 papers · 2 filters

math.NT2014★ 13 cited

Long gaps between primes

Kevin Ford, Ben Green, Sergei Konyagin +2

Let $p_{n}$ denotes the $n$ -th prime. We prove that $p_{n + 1} \leq X max (p_{n + 1} - p_{n}) ≫ \frac{lo g X lo g lo g X lo g lo g lo g lo g X}{lo g lo g lo g X}$ for sufficiently large $…

math.NT2014

Narrow progressions in the primes

Terence Tao, Tamar Ziegler

In a previous paper of the authors, we showed that for any polynomials $P_{1}, \dots, P_{k} \in Z [m]$ with $P_{1} (0) = \dots = P_{k} (0)$ and any subset $A$ of the primes in $[N] = \{1,…

math.NT2014★ 3 cited

The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture

Terence Tao

For each prime $p$ , let $n (p)$ denote the least quadratic nonresidue modulo $p$ . Vinogradov conjectured that $n(p) = O(p^\eps)$ for every fixed $\eps>0$. This conjecture follows fr…

math.NT2014★ 16 cited

Large gaps between consecutive prime numbers

Kevin Ford, Ben Green, Sergei Konyagin +1

Let $G (X)$ denote the size of the largest gap between consecutive primes below $X$ . Answering a question of Erdos, we show that $$G(X) \geq f(X) \frac{\log X \log \log X \log \log…