Sums of dilates in groups of prime order

Authors:
Alain Plagne
Affiliations:
Centre de mathématiques laurent schwartz, École polytechnique, 91128 palaiseau cedex, france (e-mail: plagne@math.polytechnique.fr)
Venue:
Combinatorics, Probability and Computing
Year:
2011

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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 â聤聜 â聞陇/pâ聞陇 is not too large (with respect to p), then | + t â聥聟 | is significantly larger than 2|| (unless |t| = 3). In the important case |t| = 2, we obtain for instance | + t â聥聟 | â聣楼 2.08 ||-2.