Algebraic independence of logarithmic singularities of some complex functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Radziejewski, Maciej

关键词: Algebraic independence;    Singularities;    Complex functions;    Dirichlet series;    Selberg class;   

DOI  :  10.1016/j.jmaa.2013.09.005

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier. Inc. All rights reserved.

【 授权许可】

Free