arXiv subjects
Publications and source records attributed to Lev Aizenberg.
We present an elementary, short and simple proof of the validity of the Lindelöf hypothesis about the Riemann zeta-function. The obtained estimate and classical results by Bohr-Landau and Littlewood disprove Riemann's hypothesis.
In the present article we give geometric generalizations of the estimates from Chapters 5,6,7 from \cite{krem:gnus}, while extending their sharpness to new cases.
We prove that the abscissas of Bohr and Rogosinski for ordinary Dirichlet series, mapping the right half-plane into the bounded convex domain $G\subset \mathbb{C} $ are independent of the domain $G$. Furthermore, we obtain new estimates about these abscissas.
The Bohr radius for power series of holomorphic functions mapping a multidimensional Reinhardt domain into the convex domain in the complex plane is independent of this convex domain.
Generalizing the classical result of Bohr, we show that if an n-variable power series converges in an n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the moduli of the terms is less than 1 in the homothetic domain r*D, where r = 1 - (2/3)^(1/n). This constant is near to the best one for the domain D = {z: |z_1| + ... + |z_n| < 1}.