Abstract
Büchi’s nth power problem asks is there a positive integer M such that any sequence \({(x_1^n,\ldots ,x_M^n)}\) of nth powers of integers with nth difference equal to n! is necessarily a sequence of nth powers of successive integers. In this paper, we study an analogue of this problem for meromorphic functions and algebraic functions.
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T. T. H. An is supported in part by the Alexander von Humboldt Foundation and ICTP and by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED).
H.-L. Huang and J. T.-Y. Wang are partially supported in part by Taiwan’s NSC grant 99-2115-M001-001-MY2.
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An, T.T.H., Huang, HL. & Wang, J.TY. Generalized Büchi’s problem for algebraic functions and meromorphic functions. Math. Z. 273, 95–122 (2013). https://doi.org/10.1007/s00209-012-0997-9
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DOI: https://doi.org/10.1007/s00209-012-0997-9