19 citations · 99 across the 36 of their papers we have counts for
46 papers
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…
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 Möb…
Descriptive properties of the type of an irrational number
William Banks, Asma Harcharras, Dominique Lecomte
The type () of an irrational number measures the extent to which rational numbers can closely approximate . More precisely, () is the infimum over those tR…
The Generalized Riemann Hypothesis from zeros of the zeta function
William D. Banks
We show that the Generalized Riemann Hypothesis for all Dirichlet L-functions is a consequence of certain conjectural properties of the zeros of the Riemann zeta function. Converse…
Comparing zeros of distinct Dirichlet L-functions
William D. Banks
For any , we show that there are constants that depend only on for which the following property holds. If are two distinct primitive Dirichlet…
The Riemann Hypothesis via the generalized von Mangoldt Function
William D. Banks, Saloni Sinha
Gonek, Graham, and Lee have shown recently that the Riemann Hypothesis (RH) can be reformulated in terms of certain asymptotic estimates for twisted sums with von Mangoldt function…