3 papers
math.NT2026
Counting zeros of Artin -functions
Chiara Bellotti, Peng-Jie Wong
In this article, assuming Artin's (holomorphy) conjecture, we establish an explicit asymptotic formula for the number of non-trivial zeros, up to any given height , of Art…
math.NT2026
Zero-free regions inspired by work of Heath-Brown
Chiara Bellotti, Tim Trudgian, Andrew Yang
We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to p…
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…