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Sums of Dilates in Groups of Prime Order
Published online by Cambridge University Press: 06 October 2011
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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