Algebraic independence of logarithmic singularities of some complex functions |
| |
Authors: | Maciej Radziejewski |
| |
Affiliation: | Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, PL-61-614 Poznań, Poland |
| |
Abstract: | We show that algebraic independence of some complex functions of one variable over regular functions implies their algebraic independence over a larger ring, containing complex powers of regular functions. Based on this we obtain a generalization of a special case of the theorem of Kaczorowski and Perelli on functional independence of logarithms of functions in the Selberg class. As an application we state a new result on oscillations of arithmetical functions. |
| |
Keywords: | Algebraic independence Singularities Complex functions Dirichlet series Selberg class |
本文献已被 ScienceDirect 等数据库收录! |