The paper claims a conditional proof of convergence for the alternating Erdős series, but the proof relies on an invalid integral representation and a false Hölder continuity assertion.
Khintchine inequality on normed spaces and the application to Banach-Mazur distance
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abstract
We establish variant Khintchine inequalities on normed spaces of Hanner type and cotype, in which the Rademacher distribution corresponding to classical Khintchine inequality is replaced by general symmetric distributions. The proof involves the $p$-barycenter and Birkhoff's ergodic theorem. More importantly, by employing these Khintchine inequalities, we get some lower bounds for Banach-Mazur distance between $l^p$-ball and a general centrally symmetric convex body.
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math.GM 1years
2025 1verdicts
REJECT 1representative citing papers
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Holder continuity of an alternating Erdos series on prime K-tuples
The paper claims a conditional proof of convergence for the alternating Erdős series, but the proof relies on an invalid integral representation and a false Hölder continuity assertion.