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${session.getAttribute("locale")}5Linear independence of values of Tschakaloff series
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∞_{v=0}q^{-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]]>Algebraic independence of Mahler functions via radial asymptotics
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2)F(z^{4}) +z^{4}F(z^{16})=0. Specifically, we prove that the functions F(z), F(z^{4}), F′(z), and F′(z^{4}) 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]]>An asymptotic approach in Mahler's method
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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]]>Degree-one Mahler functions: asymptotics, applications and speculations
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k^{n}, 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]]>Irrationality measures for certain q-mathematical constants
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Sat 24 Mar 2018 08:06:59 AEDT]]>Transcendence over meromorphic functions
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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]]>