Sums of dilates over groups of prime order

Journal article

For p prime, 𝐴⊆ℤ/𝑝⁢ℤ and 𝜆∈ℤ, the sum of dilates 𝐴+𝜆·𝐴 is defined by 𝐴+𝜆·𝐴={𝑎+𝜆⁢𝑎′:𝑎,𝑎′∈𝐴}. The basic problem on such sums of dilates asks for the minimum size of |𝐴+𝜆·𝐴| for given 𝜆, A of given density 𝛼, and p tending to infinity. We investigate this problem for 𝛼 fixed and 𝜆 tending to infinity, proving near-optimal bounds in this case.

Authors: Conlon, D; Lim, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Taylor & Francis
• Journal: American Mathematical Monthly
• Volume: 132
• Issue: 9
• Pages: 848-855
• Publication date: 2025-09-08
• Acceptance date: 2024-09-24
• DOI: 10.1080/00029890.2025.2540255
• EISSN: 1930-0972
• ISSN: 0002-9890
• Language: English