- Title
- On theorems of Gelfond and Selberg concerning integral-valued entire functions
- Creator
- Bundschuh, Peter; Zudilin, W.
- Relation
- Journal of Approximation Theory Vol. 130, Issue 2, p. 164-178
- Publisher Link
- http://dx.doi.org/10.1016/j.jat.2004.07.005
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 2004
- Description
- For each s ∈ ℕ define the constant θs 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).
- Subject
- integer valued function; polynomial interpolation; group structure arithmetic method; Selberg integral; entire function
- Identifier
- http://hdl.handle.net/1959.13/934896
- Identifier
- uon:11931
- Identifier
- ISSN:0021-9045
- Language
- eng
- Full Text
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