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Sums of Dilates in Groups of Prime Order

Published online by Cambridge University Press:  06 October 2011

ALAIN PLAGNE
ALAIN PLAGNE*
Affiliation:
Centre de Mathématiques Laurent Schwartz, École polytechnique, 91128 Palaiseau Cedex, France (e-mail: plagne@math.polytechnique.fr)
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Abstract

We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if t is an integer different from 0, 1 or −1 and if ⊂ ℤ/pℤ is not too large (with respect to p), then | + t ⋅ | is significantly larger than 2|| (unless |t| = 3). In the important case |t| = 2, we obtain for instance | + t ⋅ | ≥ 2.08 ||−2.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 6 , November 2011 , pp. 867 - 873
Copyright
Copyright © Cambridge University Press 2011

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