180 citations · 357 across the 58 of their papers we have counts for
67 papers
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 , namely for all $x\geqslant…
Explicit RIP matrices: an update
Kevin Ford, Denka Kutzarova, George Shakan
Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $\varepsilon=3.26…
Cycle type of random permutations: A toolkit
Kevin Ford
We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly P…
A Hardy-Ramanujan type inequality for shifted primes and sifted sets
Kevin Ford
We establish an analog of the Hardy-Ramanujan inequality for counting members of sifted sets with a given number of distinct prime factors. In particular, we establish a bound for…
Gaps between totients
Kevin Ford, Sergei Konyagin
We study the set D of positive integers d for which the equation has infinitely many solution pairs (a,b), where is Euler's totient function. We show that the min…
Sets whose differences avoid squares modulo m
Kevin Ford, Mikhail R. Gabdullin
We prove that if arbitrarily slowly, then for almost all and any such that does not contain non-zero quadratic residues we ha…