Geodesic
On a~strengthening of~certain theorems of~Gelfond on the integer-valuedness of~analytic functions
Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 186-207.

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We consider entire functions of finite order (greater than or equal to 1) which take rational integer values at the points of a rather general discrete set. We show that under certain conditions all such functions can only be exponential polynomials of a special form.
Keywords: entire functions of finite order, discrete set, exponential polynomials. 
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A. Y. Yanchenko. On a~strengthening of~certain theorems of~Gelfond on the integer-valuedness of~analytic functions. Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 186-207. http://geodesic.mathdoc.fr/item/IM2_2020_84_1_a6/

[1] G. Pólya, “Ueber ganzwertige ganze Funktionen”, Rend. Circ. Mat. Palermo, 40 (1915), 1–16 | DOI | Zbl

[2] A. Gelfond, “Sur un théorème de M. G. Pólya”, Atti Accad. Naz. Lincei. Rend., 10 (1929), 569–574 | Zbl

[3] A. O. Gelfond, “O tselochislennosti analiticheskikh funktsii”, Dokl. AN SSSR, 81 (1951), 341–344 | MR | Zbl

[4] I. P. Rochev, “A generalization of Gelfond's and Waldschmidt's theorems on integer-valued entire functions”, Sb. Math., 202:8 (2011), 1207–1229 | DOI | DOI | MR | Zbl

[5] M. Welter, “Sur un théorème de Gel'fond–Selberg et une conjecture de Bundschuh–Shiokawa”, Acta Arith., 116:4 (2005), 363–385 | DOI | MR | Zbl

[6] B. Ja. Levin, Distribution of zeros of entire functions, Transl. Math. Monogr., 5, Amer. Math. Soc., Providence, RI, 1964, viii+493 pp. | MR | MR | Zbl | Zbl

[7] A. O. Gelfond, Transcendental and algebraic numbers, Dover Publications, Inc., New York, 1960, vii+190 pp. | MR | MR | Zbl | Zbl

[8] A. O. Gelfond, Differenzenrechnung, Hochschulbücher für Mathematik, 41, VEB Deutscher Verlag der Wissenschaften, Berlin, 1958, viii+336 pp. | MR | MR | Zbl | Zbl

[9] S. Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, MA–London–Don Mills, ON, 1966, vi+105 pp. | MR | Zbl