https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11921 ∞_v=0q^-v(v+1)/2_z^v, |q| >1. One of the open problems is proving linear independence of the values of T_q(z) with different q. The only result obtained in this direction, in [1], is very restrictive. We refer the interested reader to the survey [2] for an account of known linear and algebraic independence results for values of Tschakaloff and other q-series.]]> Wed 11 Apr 2018 15:43:50 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:23973 2)F(z⁴) +z⁴F(z¹⁶)=0. Specifically, we prove that the functions F(z), F(z⁴), F′(z), and F′(z⁴) are algebraically independent over ℂ(z). An application of a celebrated result of Ku. Nishioka then allows one to replace ℂ(z) by ℚ when evaluating these functions at a nonzero algebraic number α in the unit disc.]]> Wed 11 Apr 2018 15:22:41 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:30913 z, but also over Cz(M), where (M) is the set of meromorphic functions. Several examples and corollaries are given, with special attention to nonnegative regular functions.]]> Wed 11 Apr 2018 15:20:26 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:39110 kⁿ, where k is the base of the Mahler function, as well as some applications concerning transcendence and algebraic independence. For example, we show that the generating function of the Thue–Morse sequence and any Mahler function (to the same base) which has a nonzero Mahler eigenvalue are algebraically independent over C(z). Finally, we discuss asymptotic bounds towards generic points on the unit circle.]]> Tue 10 May 2022 14:26:34 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10333 Sat 24 Mar 2018 08:06:59 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:30904 F(z) ϵ C[[z]] is a power series with coefficients from a finite set, then F(z) is either rational or it is transcendental over the field of meromorphic functions.]]> Sat 24 Mar 2018 07:30:39 AEDT ]]>