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math.NT2024
Improved estimates for the argument and zero-counting function of the Riemann zeta-function
Chiara Bellotti, Peng-Jie Wong
In this article, we improve the recent work of Hasanalizade, Shen, and Wong by establishing \[ \left| N (T) - \frac{T}{ 2 π} \log \left( \frac{T}{2πe}\right) \right|\le 0.10076\log…
math.NT2024
An explicit log-free zero density estimate for the Riemann zeta-function
Chiara Bellotti
We will provide an explicit log-free zero-density estimate for of the form . In particular, this estimate becomes the sharpest known explicit zero-den…