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Sharpening an Estimate of the Size of the Sumset of a Convex Set |
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| Authors: | Ol’mezov K I |
| Institution: | 1.Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, 141701, Russia ; |
| Abstract: | A finite set A = {a1 < … <an}? ? is said to be convex if the sequence (ai ? ai?1)ni=2 is strictly increasing. Using an estimate of the additive energy of convex sets, one can estimate the size of the sumset as ∣A + A∣ ? ∣A∣102/65, which slightly sharpens Shkredov’s latest result ∣A + A∣ ? ∣A∣58/37. |
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