Ably, Mohammed Entire functions with values in a number field. (Fonctions entières à valeurs dans un corps de nombres.) (English. French summary) Zbl 1219.11045 Bull. Soc. Math. Fr. 139, No. 2, 243-270 (2011). Let \(\Gamma\) be an additive subgroup of maximal rank in a number field \(k\). The author proves that any entire function on \(\Gamma\) with integer values in a finite extension of \(k\) which has both sufficiently slow analytical and arithmetical growth is a polynomial. This result extends a well-known theorem of Pólya. Moreover, it is proved that this result is optimal up to a constant. The proof uses a transcendental method. The construction of suitable interpolation polynomials plays an important role. Reviewer: Maurice Mignotte (Strasbourg) Cited in 1 Document MSC: 11C08 Polynomials in number theory 11H06 Lattices and convex bodies (number-theoretic aspects) 30D15 Special classes of entire functions of one complex variable and growth estimates Keywords:number field; entire function; polynomial; lattice; interpolation PDF BibTeX XML Cite \textit{M. Ably}, Bull. Soc. Math. Fr. 139, No. 2, 243--270 (2011; Zbl 1219.11045) Full Text: DOI Link