T. Tao

activity

20202024

most citedHigher uniformity of bounded multiplicative functions in short intervals on average

15 citations · 34 across the 10 of their papers we have counts for

collaborators

10 papers

math.NT2024★ 1 cited

On several irrationality problems for Ahmes series

Vjekoslav Kovač, Terence Tao

Using basic tools of mathematical analysis and elementary probability theory we address several problems on the irrationality of series of distinct unit fractions, $\sum_{k} 1/ a_{k}$ .…

math.NT2023

The convergence of an alternating series of Erdős, assuming the Hardy--Littlewood prime tuples conjecture

Terence Tao

It is an open question of Erdős as to whether the alternating series $\sum_{n = 1}^{\infty} \frac{( - 1 ) ^{n} n}{p _{n}}$ is (conditionally) convergent, where $p_{n}$ denotes the $n^{\mathrm{th}…

math.NT2023★ 1 cited

A lower bound on the mean value of the Erdős-Hooley Delta function

Kevin Ford, Dimitris Koukoulopoulos, Terence Tao

We give an improved lower bound for the average of the Erdős-Hooley function $Δ (n)$ , namely $\sum_{n \leq x} Δ (n) ≫_{ε} x (lo g lo g x)^{1 + η - ε}$ for all $x\geqslant…

math.PR2023

Sums of GUE matrices and concentration of hives from correlation decay of eigengaps

Hariharan Narayanan, Scott Sheffield, Terence Tao

Associated to two given sequences of eigenvalues $λ_{1} \geq \dots \geq λ_{n}$ and $μ_{1} \geq \dots \geq μ_{n}$ is a natural polytope, the polytope of augmented hives with the specified b…

math.NT2023★ 12 cited

Sumsets and entropy revisited

Ben Green, Freddie Manners, Terence Tao

The entropic doubling $σ_{ent} [X]$ of a random variable $X$ taking values in an abelian group $G$ is a variant of the notion of the doubling constant $σ [A]$ of a fin…

math.NT2023★ 5 cited

An upper bound on the mean value of the Erdős-Hooley Delta function

Dimitris Koukoulopoulos, Terence Tao

The Erdős-Hooley Delta function is defined for $n \in N$ as $Δ (n) = sup_{u \in R} # {d ∣ n : e^{u} < d \leq e^{u + 1}}$ . We prove that $\sum_{n\le x} Δ(n) \ll x(\log\log x)^{1…

math.DS2023

The structure of totally disconnected Host--Kra--Ziegler factors, and the inverse theorem for the $U^{k}$ Gowers uniformity norms on finite abelian groups of bounded torsion

Asgar Jamneshan, Or Shalom, Terence Tao

Let $Γ$ be a countable abelian group, let $k \geq 1$ , and let $X = (X, X, μ, T)$ be an ergodic $Γ$ -system of order $k$ in the sense of Host--Kra--Ziegler. The $Γ$ -syst…

math.DS2023

A Host--Kra $F_{2}^{ω}$ -system of order $5$ that is not Abramov of order $5$ , and non-measurability of the inverse theorem for the $U^{6} (F_{2}^{n})$ norm

Asgar Jamneshan, Or Shalom, Terence Tao

It was conjectured by Bergelson, Tao, and Ziegler \cite{btz} that every Host--Kra $\F_p^ω$-system of order $k$ is an Abramov system of order $k$ . This conjecture has been verified…

math.NT2023

Infinite partial sumsets in the primes

Terence Tao, Tamar Ziegler

We show that there exist infinite sets $A = {a_{1}, a_{2}, \dots}$ and $B = {b_{1}, b_{2}, \dots}$ of natural numbers such that $a_{i} + b_{j}$ is prime whenever $1 \leq i < j$ .

math.NT2020★ 15 cited

Higher uniformity of bounded multiplicative functions in short intervals on average

Kaisa Matomäki, Maksym Radziwiłł, Terence Tao +2

Let $λ$ denote the Liouville function. We show that, as $X \to \infty$ , $$\int_{X}^{2X} \sup_{\substack{P(Y)\in \mathbb{R}[Y]\\ deg(P)\leq k}} \Big | \sum_{x \leq n \leq x…