Improved bounds Δ(s) ≪ s^{-(3/2-ε)} (upper) and Δ(s) ≫ (log s) s^{-3/2} (lower) for the minimal triangle area with s points in the unit disk.
232:2, Elsevier, 1999, pp 272--292
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Lower bounds on coincidence points for multiplicative and additive functions are obtained, varying with period length and worst-case growth rates of consecutive value ratios.
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New bounds for the Heilbronn triangle problem
Improved bounds Δ(s) ≪ s^{-(3/2-ε)} (upper) and Δ(s) ≫ (log s) s^{-3/2} (lower) for the minimal triangle area with s points in the unit disk.
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On the pointwise periodicity of multiplicative and additive functions
Lower bounds on coincidence points for multiplicative and additive functions are obtained, varying with period length and worst-case growth rates of consecutive value ratios.