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Christoph Aistleitner, István Berkes, Kristian Seip, Michel Weber, Convergence of series of dilated functions, spectral norms of GCD matrices,Acta Arithmetica168( · 2015 · DOI 10.4064/aa168-3-2

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Counterexamples for lacunary dilates via dyadic spike blocks

math.CA · 2026-04-20 · unverdicted · novelty 8.0

Dyadic spike blocks yield counterexamples where lacunary averages diverge to infinity a.e. for mean-zero functions in all L^q and for L^p functions, resolving Erdős problems #995 and #996 negatively.

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  • Counterexamples for lacunary dilates via dyadic spike blocks math.CA · 2026-04-20 · unverdicted · none · ref 3

    Dyadic spike blocks yield counterexamples where lacunary averages diverge to infinity a.e. for mean-zero functions in all L^q and for L^p functions, resolving Erdős problems #995 and #996 negatively.