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${session.getAttribute("locale")}5On theorems of Gelfond and Selberg concerning integral-valued entire functions
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s with the following properties: if an entire function g(z) of type t(g) <θ_{s} satisfies g^{(σ)}(z) ∈ ℤ for σ = 0, 1,..., s - 1 and z = 0, 1, 2,..., then g is a polynomial; conversely, for any δ > 0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g) <θ_{s} + δ. The result θ_{1} = log 2 is known due to Hardy and Pólya. We provide the upper bound θ_{s} ≤ πs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941).]]>Wed 11 Apr 2018 13:50:25 AEST]]>Rational approximations to a q-analogue of π and some other q-series.
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Sat 24 Mar 2018 08:25:20 AEDT]]>Irrationality measures for certain q-mathematical constants
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Sat 24 Mar 2018 08:06:59 AEDT]]>