6 papers
Estimates for -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 and in the neighbourhood of the…
Explicit estimates for in the critical strip under the Riemann Hypothesis
Aleksander Simonič
Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for right to the critical line. As an application we make explicit Titchmarsh's…
Explicit zero density estimate for the Riemann zeta-function near the critical line
Aleksander Simonič
In 1946, A. Selberg proved where is the number of nontrivial zeros of the Riemann zeta-function with…
Lehmer pairs and derivatives of Hardy's -function
Aleksander Simonič
Occurrences of very close zeros of the Riemann zeta function are strongly connected with Lehmer pairs and with the Riemann Hypothesis. The aim of the present note is to derive a co…
Elementary approach to the Hartogs extension theorem
Aleksander Simonič
In this paper we present a proof of Hartogs' extension theorem, following T. Sobieszek's paper from 2003. Hartogs' theorem provides a large class of domains where holomorphic funct…
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…