This article is cited in 1 paper

On the algebraic independence of functions of a certain class

P. Yu. Kozlov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We consider Ramanujan functions and a family of functions whose properties are close to those of Ramanujan functions. We prove the algebraic independence of these functions over the field of rational functions with complex coefficients. We also prove a bound for the multiplicity of the zeros of polynomials in these functions.

Keywords: algebraic independence, Ramanujan functions, bound for the multiplicity of the zeros of polynomials.

UDC: 511

MSC: Primary 11J89; Secondary 13B25

Received: 06.11.2011

DOI: 10.4213/im7932

 English version: Izvestiya: Mathematics, 2013, 77:1, 20–29

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