Recent zbMATH articles in MSC 30D20 https://www.zbmath.org/atom/cc/30D20 2022-05-16T20:40:13.078697Z Werkzeug The fundamental theorem of algebra and Liouville's theorem geometrically revisited https://www.zbmath.org/1483.30027 2022-05-16T20:40:13.078697Z "Almira, Jose Maria" https://www.zbmath.org/authors/?q=ai:almira.jose-maria "Romero, Alfonso" https://www.zbmath.org/authors/?q=ai:romero.alfonso Summary: If $$f(z)$$ is either a polynomial with no zeroes or a bounded entire function, then a Riemannian metric $$g_f$$ is constructed on the complex plane $$\mathbb{C}$$. This metric $$g_f$$ is shown to be flat and geodesically complete. Therefore, the Riemannian manifold $$(\mathbb{C}, g_f)$$ must be isometric to $$(\mathbb{C}, |dz|^2)$$, which implies that $$f(z)$$ is a constant. Uniqueness of differential $$q$$-shift difference polynomials of entire functions https://www.zbmath.org/1483.30062 2022-05-16T20:40:13.078697Z "Mathai, Madhura M." https://www.zbmath.org/authors/?q=ai:mathai.madhura-m "Manjalapur, Vinayak V." https://www.zbmath.org/authors/?q=ai:manjalapur.vinayak-v Summary: In this paper, we prove the uniqueness theorems of differential $$q$$-shift difference polynomials of transcendental entire functions. On conditions of the completeness of some systems of Bessel functions in the space $$L^2 ((0;1); x^{2p} dx)$$ https://www.zbmath.org/1483.42023 2022-05-16T20:40:13.078697Z "Khats, R. V." https://www.zbmath.org/authors/?q=ai:khats.r-v In this paper the author gives necessary and sufficient conditions for the system $$\{x^{-p-1}\sqrt{x\rho_k}J_\nu(x\rho_k): k \in \mathbb{N}\}$$ to be complete in the weighted space $$L^2((0,1), x^{2p} dx)$$. Here $$J_\nu$$ is the first kind Bessel function of index $$\nu \geq \frac{1}{2}$$, $$p \in \mathbb{R}$$ and $$\rho_k : k \in \mathbb{N}$$ is an arbitrary sequence of distinct nonzero complex numbers. The fact that $$\rho_k$$ can be arbitrary had already been considered by \textit{B. V. Vynnyts'kyi} and \textit{R. V. Khats'} [Eurasian Math. J. 6, No. 1, 123--131 (2015; Zbl 1463.30015)]. In the present paper, he gives new conditions which depend only on properties of the $$\rho_k$$. Reviewer: Ursula Molter (Buenos Aires)