19 citations · 99 across the 36 of their papers we have counts for
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math.NT2014★ 1 cited
Convolutions with probability distributions, zeros of L-functions, and the least quadratic nonresidue
William D. Banks, Konstantin A. Makarov
Let be a probability distribution. Under certain mild conditions we show that $$ \lim_{x\to\infty}x\sum_{n=1}^\infty \frac{d^{*n}(x)}{n}=1,\qquad\text{where}\quad d^{*n}:=\unde…
math.NT2014
Fractional parts of Dedekind sums
William D. Banks, Igor E. Shparlinski
Using a recent improvement by Bettin and Chandee to a bound of Duke, Friedlander and Iwaniec~(1997) on double exponential sums with Kloosterman fractions, we establish a uniformity…
math.NT2014★ 14 cited
On limit points of the sequence of normalized prime gaps
William D. Banks, Tristan Freiberg, James Maynard
Let denote the th smallest prime number, and let denote the set of limit points of the sequence of normali…