5 papers
Explicit bounds for the Riemann zeta function and a new zero-free region
Chiara Bellotti
We prove that for and . As a consequence, we improve the explicit zero-free region for , sho…
On the generalised Dirichlet divisor problem
Chiara Bellotti, Andrew Yang
We improve unconditional estimates on , the remainder term of the generalised divisor function, for large . In particular, we show that $Δ_k(x) \ll x^{1 - 1.889k^{-2/3}}…
New bounds for numbers of primes in element orders of finite groups
Chiara Bellotti, Thomas Michael Keller, Timothy S. Trudgian
Let denote the maximal number of different primes that may occur in the order of a finite solvable group , all elements of which have orders divisible by at most dist…
A conditional result on exponential sums over primes in short intervals
Chiara Bellotti, Giuseppe Puglisi
The aim of this work is to illustrate a conditional result involving the exponential sums over primes in short intervals under the assumption that both the Generalized Riemann Hypo…
Elementary methods in the study of Deuring-Heilbronn Phenomenon
Chiara Bellotti, Giuseppe Puglisi
The aim of this work is to improve some elementary results regarding both the Deuring-Phenomenon and the Heilbronn-Phenomenon. We will give better estimates regarding both the infl…