The sum-product conjecture is false for real numbers, disproved via constructions of sets A with max(|A+A|, |AA|) ≤ |A|^{2-c} for absolute c > 0.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Proves |f(A)| <= |A|^{k-c} for monic degree-k polynomials f in the Minkowski sum-product sense, including a bound for AA+A.
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The sum-product conjecture is false for real numbers
The sum-product conjecture is false for real numbers, disproved via constructions of sets A with max(|A+A|, |AA|) ≤ |A|^{2-c} for absolute c > 0.
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Power-Saving Bounds For Monic Minkowski Polynomials
Proves |f(A)| <= |A|^{k-c} for monic degree-k polynomials f in the Minkowski sum-product sense, including a bound for AA+A.