19 citations · 99 across the 36 of their papers we have counts for
3 papers · 2 filters
Consecutive primes in tuples
William D. Banks, Tristan Freiberg, Caroline L. Turnage-Butterbaugh
In a recent advance towards the Prime -tuple Conjecture, Maynard and Tao have shown that if is sufficiently large in terms of , then for an admissible -tuple $\mathcal…
On Gauss sums and the evaluation of Stechkin's constant
William D. Banks, Igor E. Shparlinski
For the Gauss sums which are defined by S_n(a,q) := \sum_{x (mod q)} e(ax^n/q), Stechkin (1975) conjectured that the quantity A := \sup_{n,q\ge 2} \max_{\gcd(a,q)=1} |S_n(a,q)|/q^(…
Optimal primitive sets with restricted primes
William D. Banks, Greg Martin
A set of natural numbers is primitive if no element of the set divides another. Erdős conjectured that if S is any primitive set, then \sum_{n\in S} 1/(n log n) \le \sum_{n\in ¶} 1…