Hooley, ‘On the intervals between numbers that are sum of two squares’, Acta Math

· 1971

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math.NT · 2025-05-29 · unverdicted · novelty 6.0

For fixed nonzero a, the set S(△, □₂, a) contains ≳ x^{5/6-ε} elements inside every interval of length H_a x^{5/6} log^{19} x for large x.

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Gaps between quadratic forms math.NT · 2025-05-29 · unverdicted · none · ref 6
For fixed nonzero a, the set S(△, □₂, a) contains ≳ x^{5/6-ε} elements inside every interval of length H_a x^{5/6} log^{19} x for large x.