On a Refinement of the Schneider–Lang theorem

We consider some arithmetic properties of values of meromorphic functions , …, such that each of is algebraically dependent over a field of algebraic numbers, , with the functions . We show that if all are meromorphic of finite order, then either they all are rational functions, or they all are rati...

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Bibliographic Details
Published in:Mathematical Notes 2023-06, Vol.113 (5-6), p.804-814
Main Authors: Podkopaeva, V. A., Yanchenko, A. Ya
Format: Article
Language:English
Subjects:
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639/766/530
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Elliptic functions
Mathematics
Mathematics and Statistics
Meromorphic functions
Rational functions
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Summary:We consider some arithmetic properties of values of meromorphic functions , …, such that each of is algebraically dependent over a field of algebraic numbers, , with the functions . We show that if all are meromorphic of finite order, then either they all are rational functions, or they all are rational functions of some exponential, or they all are elliptic functions, or there exists a discrete set such that the number of points such that all lie in is finite.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S000143462305022X