Algebraic independence of logarithmic singularities of some complex functions (Q2260363)

The author shows that the 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, he obtains a generalization of a special case of the theorem of \textit{J. Kaczorowski} and \textit{A. Perelli} [Am. J. Math. 120, No. 2, 289--303 (1998; Zbl 0905.11036); in: Number theory in progress. Proceedings of the international conference organized by the Stefan Banach International Mathematical Center in honor of the 60th birthday of Andrzej Schinzel, Zakopane, Poland, 1997. Volume 2: Elementary and analytic number theory. Berlin: de Gruyter. 953--992 (1999; Zbl 0929.11028)] on functional independence of logarithms of functions in the Selberg class. As an application he states a new result on oscillations of arithmetical functions.