Sums of transcendental dilates

Creators: Conlon, David; Lim, Jeck

Abstract

We show that there is an absolute constant c > 0 such that |A + λ • A| ⩾ e^(c√log|A)| |A| for any finite subset A of ℝ and any transcendental number λ ∈ ℝ. By a construction of Konyagin and Łaba, this is best possible up to the constant c.

Additional Information

© 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. Research supported by NSF Award DMS-2054452 and partially supported by an NUS Overseas Graduate Scholarship.

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Resource type: Journal Article
Publisher: London Mathematical Society
Published in: Bulletin of the London Mathematical Society, ISSN: 0024-6093.

Created:: August 22, 2023
Modified:: October 20, 2023