Kevin Ford

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math.NT2025

Large prime gaps and probabilistic models

William Banks, Kevin Ford, Terence Tao

We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a…

math.NT2025

Zero-free regions for the Riemann zeta function

Kevin Ford

We improve existing explicit bounds of Vinogradov-Korobov type for zero-free regions of the Riemann zeta function, both for large height t and for every t. A primary input is an ex…

math.NT2024

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

Kevin Ford, Dimitris Koukoulopoulos, Terence Tao

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

Large prime gaps and probabilistic models

Zero-free regions for the Riemann zeta function

A lower bound on the mean value of the ErdÅs-Hooley Delta function

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