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Published August 18, 2023 | public
Journal Article

Sums of transcendental dilates


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.

Additional details

August 22, 2023
October 20, 2023