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Entire functions having a concordant value sequence

Abstract:

A classic theorem of Pólya shows that 2z is, in a strong sense, the "smallest" transcendental entire function that is integer valued on ℕ. An analogous result of Gel'fond concerns entire functions that are integer valued on the set Xa = {an: n ∈ ℕ}, where a ∈ ℕ, |a| ≥ 2. Let X = ℕ or X = Xa and k ∈ ℕ or k = ∞. This paper pursues analogous results for entire functions f having the following property: on any finite subset D of X with #D ≤ k + 1, the values f(z),z ∈ D admit interpolation by an e...

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Publication status:
Published

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Publisher copy:
10.1007/BF02787411

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ISRAEL JOURNAL OF MATHEMATICS
Volume:
134
Issue:
1
Pages:
317-343
Publication date:
2003-01-01
DOI:
EISSN:
1565-8511
ISSN:
0021-2172
URN:
uuid:44cfd2d2-b003-499d-968f-f4710560e972
Source identifiers:
188531
Local pid:
pubs:188531
Language:
English

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