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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

On the distribution of sums of residues


Author: Jerrold R. Griggs
Journal: Bull. Amer. Math. Soc. 28 (1993), 329-333
MSC: Primary 11P83; Secondary 11B50
MathSciNet review: 1183998
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Abstract: We generalize and solve the $ {\bmod \;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 _i}{a_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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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1993-00382-3
PII: S 0273-0979(1993)00382-3
Article copyright: © Copyright 1993 American Mathematical Society