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On the distribution of sums of residues

Jerrold R. Griggs
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Abstract

We generalize and solve the $\roman{mod}\,q$ analogue of a problem of Littlewood and Offord, raised by Vaughan and Wooley, concerning the distribution of the $2^n$ sums of the form $\sum_{i=1}^n\varepsilon_ia_i$, where each $\varepsilon_i$ is $0$ or $1$. For all $q$, $n$, $k$ we determine the maximum, over all reduced residues $a_i$ and all sets $P$ consisting of $k$ arbitrary residues, of the number of these sums that belong to $P$.

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Jerrold R. Griggs. 1993-04-01. On the distribution of sums of residues. https://arxiv.org/abs/math/9304211

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