Entire functions which are infinitely integer-valued at a finite number of points
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- by P. Lockhart and E. G. Straus PDF
- Trans. Amer. Math. Soc. 293 (1986), 643-654 Request permission
Abstract:
This paper determines arithmetic limits for the growth rates of entire functions which are infinitely integer valued on a finite set $S$. The characterization of such functions with growth rate less than the arithmetic limit is complete if there exist exponential polynomials which are infinitely integer valued on $S$.References
- Alan Baker, Transcendental number theory, Cambridge University Press, London-New York, 1975. MR 0422171, DOI 10.1017/CBO9780511565977
- Afton H. Cayford, A class of integer valued entire functions, Trans. Amer. Math. Soc. 141 (1969), 415–432. MR 244486, DOI 10.1090/S0002-9947-1969-0244486-1
- A. H. Cayford and E. G. Straus, On differential rings of entire functions, Trans. Amer. Math. Soc. 209 (1975), 283–293. MR 382671, DOI 10.1090/S0002-9947-1975-0382671-1
- B. Ja. Levin, Distribution of zeros of entire functions, American Mathematical Society, Providence, R.I., 1964. MR 0156975, DOI 10.1090/mmono/005
- L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan & Co., Ltd., London, 1951. MR 0043339
- L. D. Neidleman and E. G. Straus, Functions whose derivatives at one point form a finite set, Trans. Amer. Math. Soc. 140 (1969), 411–422. MR 241644, DOI 10.1090/S0002-9947-1969-0241644-7
- Daihachiro Sato, Two counterexamples and some remarks on integer-valued functions, Sūgaku 14 (1962/63), 95–98 (Japanese). MR 150302
- Daihachiro Sato and Ernst G. Straus, On the rate of growth of Hurwitz functions of a complex or $p$-adic variable, J. Math. Soc. Japan 17 (1965), 17–29. MR 192030, DOI 10.2969/jmsj/01710017
- E. G. Straus, On entire functions with algebraic derivatives at certain algebraic points, Ann. of Math. (2) 52 (1950), 188–198. MR 35822, DOI 10.2307/1969518
- Ernst G. Straus, On the polynomials whose derivatives have integral values at the integers, Proc. Amer. Math. Soc. 2 (1951), 23–27. MR 40481, DOI 10.1090/S0002-9939-1951-0040481-8
- E. G. Straus, Differential rings of meromorphic functions, Acta Arith. 21 (1972), 271–284. MR 308418, DOI 10.4064/aa-21-1-271-284 —, Differential rings of meromorphic functions of a non-Archimedean variable, Diophantine approximation and its applications (Proc. Conf. Washington, D. C., 1972), Academic Press, New York, 1973, pp. 295-308.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 293 (1986), 643-654
- MSC: Primary 30D15
- DOI: https://doi.org/10.1090/S0002-9947-1986-0816316-8
- MathSciNet review: 816316