Aleksander Simonivc

activity

20152022

collaborators

4 papers

math.NT2022

Estimates for $L$ -functions in the critical strip under GRH with effective applications

Aleksander Simonič

Assuming the Generalized Riemann Hypothesis, we provide explicit upper bounds for moduli of $lo g L (s)$ and $L^{'} (s) / L (s)$ in the neighbourhood of the…

math.NT2021

Explicit estimates for $ζ (s)$ in the critical strip under the Riemann Hypothesis

Aleksander Simonič

Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $∣ ζ (s) ∣$ right to the critical line. As an application we make explicit Titchmarsh's…

math.NT2019

Explicit zero density estimate for the Riemann zeta-function near the critical line

Aleksander Simonič

In 1946, A. Selberg proved $N (σ, T) ≪ T^{1 - \frac{1}{4} (σ - \frac{1}{2})} lo g T$ where $N (σ, T)$ is the number of nontrivial zeros $ρ$ of the Riemann zeta-function with…

math.CV2015

The Ahlfors lemma and Picard's theorems

Aleksander Simonič

The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems conc…

Estimates for L-functions in the critical strip under GRH with effective applications

Explicit estimates for ζ(s) in the critical strip under the Riemann Hypothesis

Explicit zero density estimate for the Riemann zeta-function near the critical line

The Ahlfors lemma and Picard's theorems

Estimates for $L$ -functions in the critical strip under GRH with effective applications

Explicit estimates for $ζ (s)$ in the critical strip under the Riemann Hypothesis