On a strengthening of certain theorems of Gelfond on the integer-valuedness of analytic functions
- Autores: Yanchenko A.Y.1
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Afiliações:
- National Research University "Moscow Power Engineering Institute"
- Edição: Volume 84, Nº 1 (2020)
- Páginas: 207-230
- Seção: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133809
- DOI: https://doi.org/10.4213/im8686
- ID: 133809
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Resumo
We consider entire functions of finite order (greater than or equal to 1) which take rational integer values atthe points of a rather general discrete set. We show that under certain conditions all such functionscan only be exponential polynomials of a special form.
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Sobre autores
Aleksandr Yanchenko
National Research University "Moscow Power Engineering Institute"Candidate of physico-mathematical sciences, Associate professor
Bibliografia
- G. Polya, “Ueber ganzwertige ganze Funktionen”, Rend. Circ. Mat. Palermo, 40 (1915), 1–16
- A. Gelfond, “Sur un theorème de M. G. Polya”, Atti Accad. Naz. Lincei. Rend., 10 (1929), 569–574
- А. О. Гельфонд, “О целочисленности аналитических функций”, Докл. АН СССР, 81 (1951), 341–344
- И. П. Рочев, “Обобщение теорем Гельфонда и Вальдшмидта о целозначных целых функциях”, Матем. сб., 202:8 (2011), 117–138
- M. Welter, “Sur un theorème de Gel'fond–Selberg et une conjecture de Bundschuh–Shiokawa”, Acta Arith., 116:4 (2005), 363–385
- Б. Я. Левин, Распределение корней целых функций, Гостехиздат, М., 1956, 632 с.
- А. О. Гельфонд, Трансцендентные и алгебраические числа, Гостехиздат, М., 1952, 224 с.
- А. О. Гельфонд, Исчисление конечных разностей, Гостехиздат, М.–Л., 1952, 479 с.
- S. Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, MA–London–Don Mills, ON, 1966, vi+105 pp.
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