C. Bellotti

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math.NT2023

Explicit bounds for the Riemann zeta function and a new zero-free region

Chiara Bellotti

We prove that $∣ ζ (σ + i t) ∣ \leq 70.7∣ t ∣^{4.438 (1 - σ)^{3/2}} lo g^{2/3} ∣ t ∣$ for $1/2 \leq σ \leq 1$ and $∣ t ∣ \geq 3$ . As a consequence, we improve the explicit zero-free region for $ζ (s)$ , sho…

math.NT2023

On the generalised Dirichlet divisor problem

Chiara Bellotti, Andrew Yang

We improve unconditional estimates on $Δ_{k} (x)$ , the remainder term of the generalised divisor function, for large $k$ . In particular, we show that $Δ_k(x) \ll x^{1 - 1.889k^{-2/3}}…