2 papers
math.NT2026
Sign changes of the Liouville function in arithmetic progressions
Kevin Ford, Maksym RadziwiÅÅ
We show that for any , prime sufficiently large with respect to and residue class , there exist two integers $m, n \leq q^{5/2 + \…
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…