D. Polymath

activity

20092022

most citedNew equidistribution estimates of Zhang type

95 citations · 112 across the 6 of their papers we have counts for

collaborators

8 papers

math.CO2022★ 2 cited

The probability that a random triple of dice is transitive

D. H. J. Polymath

An $n$ -sided die is an $n$ -tuple of positive integers. We say that a die $(a_{1}, \dots, a_{n})$ beats a die $(b_{1}, \dots, b_{n})$ if the number of pairs $(i, j)$ such that $a_{i} > b_{j}$ is great…

math.NT2019

Effective approximation of heat flow evolution of the Riemann $ξ$ function, and a new upper bound for the de Bruijn-Newman constant

D. H. J. Polymath

For each $t \in R$ , define the entire function $H_{t} (z) := \int_{0}^{\infty} e^{t u^{2}} Φ (u) cos (z u) d u$ where $Φ$ is the super-exponentially decaying function $$ Φ(u) := \s…

math.HO2014★ 13 cited

The "bounded gaps between primes" Polymath project - a retrospective

D. H. J. Polymath

For any $m \geq 1$ , let $H_{m}$ denote the quantity $H_{m} := lim inf_{n \to \infty} (p_{n + m} - p_{n})$ , where $p_{n}$ denotes the $n^{th}$ prime; thus for instance the twin p…

math.NT2014★ 2 cited

Variants of the Selberg sieve, and bounded intervals containing many primes

D. H. J. Polymath

For any $m \geq 1$ , let $H_{m}$ denote the quantity $lim inf_{n \to \infty} (p_{n + m} - p_{n})$ . A celebrated recent result of Zhang showed the finiteness of $H_{1}$ , with the explicit boun…

math.NT2014★ 95 cited

New equidistribution estimates of Zhang type

D. H. J. Polymath

We prove distribution estimates for primes in arithmetic progressions to large smooth squarefree moduli, with respect to congruence classes obeying Chinese Remainder Theorem condit…

math.NT2010

Deterministic methods to find primes

D. H. J. Polymath

Given a large positive integer $N$ , how quickly can one construct a prime number larger than $N$ (or between $N$ and 2N)? Using probabilistic methods, one can obtain a prime number…

The probability that a random triple of dice is transitive

Effective approximation of heat flow evolution of the Riemann ξ function, and a new upper bound for the de Bruijn-Newman constant

The "bounded gaps between primes" Polymath project - a retrospective

Variants of the Selberg sieve, and bounded intervals containing many primes

New equidistribution estimates of Zhang type

Deterministic methods to find primes

Effective approximation of heat flow evolution of the Riemann $ξ$ function, and a new upper bound for the de Bruijn-Newman constant