Arithmetic Progressions in Sets of Fractional Dimension

Izabella Łaba1, Malabika Pramanik1
1Department of Mathematics, University of British Columbia, Vancouver, Canada

Tóm tắt

Let $${E \subset\mathbb{R}}$$ be a closed set of Hausdorff dimension α. Weprove that if α is sufficiently close to 1, and if E supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then E contains non-trivial 3-term arithmetic progressions.

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Tài liệu tham khảo

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