OpenAI reports singular Bernoulli convolutions at quartic Salem reciprocals
- Mathematics
For every quartic Salem number β with 1<β<2, the unbiased Bernoulli convolution with contraction parameter λ=β⁻¹ is singular with respect to Lebesgue measure.
OpenAI reports singular Bernoulli convolutions at quartic Salem reciprocals
- Mathematics
For every quartic Salem number β with 1<β<2, the unbiased Bernoulli convolution with contraction parameter λ=β⁻¹ is singular with respect to Lebesgue measure.
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Read the background
For every quartic Salem number β with 1<β<2, the unbiased Bernoulli convolution with contraction parameter λ=β⁻¹ is singular with respect to Lebesgue measure.
Why it matters
If correct, supplies singular Bernoulli convolutions at non-Pisot reciprocal parameters.
What counts as progress
Can a Bernoulli convolution be singular when the reciprocal parameter is a Salem number rather than Pisot?
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OpenAI reports singular Bernoulli convolutions at quartic Salem reciprocals