3 papers
math.NT2026
Sets of integers satisfying Bateman-Horn statistics
William Banks, Kevin Ford
In 1962, Bateman and Horn conjectured precise asymptotics for the count of positive integers n \le x for which f_1(n), ..., f_k(n) are all prime, where (f_1, ..., f_k) is an admiss…
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
Multiple sums with the Möbius function
William D. Banks, Igor E. Shparlinski
We establish nontrivial bounds for bilinear sums involving the Möbius function evaluated over solutions to a broad class of equations. Several of our results may be regarded as MÅ