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Explicit zero density estimate near unity

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arxiv 2311.05136 v1 pith:7PDSY2TH submitted 2023-11-09 math.NT

Chiara Bellotti This is my paper · ORCID
classification math.NT
keywords estimateexplicitsigmadensitydotsfirstformimprove
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abstract

We will provide the first explicit zero-density estimate for $\zeta$ of the form $N(\sigma,T)\le \mathcal{C}T^{B(1-\sigma)^{3/2}}(\log T)^C$. In particular, we improve $C$ to $10393/900=11.547\dots.$

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Cited by 1 Pith paper

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  1. On the connection between zero-free regions and the error term in the Prime Number Theorem

    math.NT 2025-07 accept novelty 7.0 of 10

    For a broad class of zero-free regions, the paper sharpens the prime number theorem error term and constructs Beurling systems showing this sharpening is nearly optimal.

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