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ENTIRE FUNCTIONS SHARING ARGUMENTS OF INTEGRALITY, I

Abstract:
Let f be an entire function that is real and strictly increasing for all sufficiently large real arguments, and that satisfies certain additional conditions, and let Xf be the set of non-negative real numbers at which f is integer valued. Suppose g is an entire function that takes integer values on Xf. We find growth conditions under which f,g must be algebraically dependent (over ℤ) on X. The result generalizes a weak form of a theorem of Pólya. © 2009 World Scientific Publishing Company.
Publication status:
Published

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Publisher copy:
10.1142/S1793042109002146

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
INTERNATIONAL JOURNAL OF NUMBER THEORY
Volume:
5
Issue:
2
Pages:
339-353
Publication date:
2009-03-05
DOI:
EISSN:
1793-7310
ISSN:
1793-0421
URN:
uuid:44be83f8-758c-4a6c-be2c-5424688ddaef
Source identifiers:
188286
Local pid:
pubs:188286
Language:
English
Keywords:

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