7 papers
Improved average and almost-all bounds for
Chiara Bellotti
In this paper we study the least positive integer such that the integers with generate . We prove that, for every $\var…
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…
A conjecture of Glasby, Praeger, and Unger on permutations of
Chiara Bellotti, Tim Trudgian
We prove a conjecture of Glasby, Praeger, and Unger concerning the symmetric group . Let denote the proportion of elements of that are pre--cycles for som…
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…
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…
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…
Explicit zero density estimate near unity
Chiara Bellotti
We will provide the first explicit zero-density estimate for of the form . In particular, we improve to $10393/900=11.547\d…