Multiplicative Sidon sets in [1,n] exist with maximal gap ≪_ε n^{10/33 + ε}.
Li,The number of primes in short intervals and numerical calculations for Harman’s sieve, preprint
2 Pith papers cite this work. Polarity classification is still indexing.
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For almost all x, the interval (x, x+h] with h=X^θ contains ≍h integers that are a prime plus an element of the lacunary sumset Aλ, for every θ>2/15+ε.
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Gaps in Multiplicative Sidon Sets II
Multiplicative Sidon sets in [1,n] exist with maximal gap ≪_ε n^{10/33 + ε}.
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Short intervals for the Romanoff-type sumset
For almost all x, the interval (x, x+h] with h=X^θ contains ≍h integers that are a prime plus an element of the lacunary sumset Aλ, for every θ>2/15+ε.