ABC sum-product theorems for Katz-Tao sets
Abstract
I prove two variants of the ABC sum-product theorem for δ-separated sets A,B,C ⊂ [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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