A. Walker

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20182020

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math.NT2018

Arithmetic Progressions with Restricted Digits

Aled Walker, Alexander Walker

For an integer $b ⩾ 2$ and a set $S \subset {0, \dots, b - 1}$ , we define the Kempner set $K (S, b)$ to be the set of all non-negative integers whose base- $b$ digital…

math.NT2018

GCD sums and sum-product estimates

Thomas F. Bloom, Aled Walker

In this note we prove a new estimate on so-called GCD sums (also called Gál sums), which, for certain coefficients, improves significantly over the general bound due to de la Bretè…