https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 On theorems of Gelfond and Selberg concerning integral-valued entire functions https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11931 s with the following properties: if an entire function g(z) of type t(g) <θs 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) <θs + δ. The result θ1 = log 2 is known due to Hardy and Pólya. We provide the upper bound θs ≤ 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. https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:15720 Sat 24 Mar 2018 08:25:20 AEDT ]]> Irrationality measures for certain q-mathematical constants https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10333 Sat 24 Mar 2018 08:06:59 AEDT ]]>