Pith. sign in

REVIEW 1 cited by

Proving the Duffin-Schaeffer conjecture without GCD graphs

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2404.15123 v2 pith:HWQJSW7P submitted 2024-04-23 math.NT

Manuel Hauke , Santiago Vazquez Saez , Aled Walker This is my paper · ORCID
classification math.NT
keywords conjecturediophantineduffin-schaefferfirstgraphsmetricproofaistleitner-borda
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthrough first argument, but simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their `quality'. We also consider the metric quantitative theory of Diophantine approximations, improving the $(\log \Psi(N))^{-C}$ error-term of Aistleitner-Borda and the first named author to $\exp(-(\log \Psi(N))^{\frac{1}{2} - \varepsilon})$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Erd\H{o}s's integer dilation approximation problem and GCD graphs

    math.NT 2025-02 accept novelty 8.0 of 10

    Erdős's integer dilation approximation problem is resolved: sets with positive logarithmic density always contain distinct α, β with |nα−β| arbitrarily small.

Pith tools