The moving-target Khintchine conjecture holds under an extra-divergence condition on psi and whenever the target centers lie in a finite set, yielding a monochromatic-denominator corollary.
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Toward Khintchine's theorem with a moving target: extra divergence or finitely centered target
The moving-target Khintchine conjecture holds under an extra-divergence condition on psi and whenever the target centers lie in a finite set, yielding a monochromatic-denominator corollary.