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arXiv · 2511.05091

Asymmetric sum-product theorems for Katz-Tao sets

Tuomas Orponen
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Abstract

I prove two variants of the $ABC$ sum-product theorem for $δ$-separated sets $A,B,C \subset [0,1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality of the sets $B,C$ need not match their non-concentration exponent. The new $ABC$ theorems are sharp under their respective hypotheses, and imply the previous one.

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Tuomas Orponen. 2026-08-20. Asymmetric sum-product theorems for Katz-Tao sets. https://arxiv.org/abs/2511.05091

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