Geodesic
On the algebraic independence of functions of a~certain class
Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 20-29

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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. 
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     author = {P. Yu. Kozlov},
     title = {On the algebraic independence of functions of a~certain class},
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P. Yu. Kozlov. On the algebraic independence of functions of a~certain class. Izvestiya. Mathematics , Tome 77 (2013) no. 1, pp. 20-29. http://geodesic.mathdoc.fr/item/IM2_2013_77_1_a2/