Abstract
LetK be a function field in one variable over ℂ anda 1,...,a m ,b non-zero elements ofK, such thatb is linearly independent froma 1,...,a m over ℂ. We show that forn sufficiently large, the equation ∑ m i=1 a i x n i has no non-constant solutions inK.
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Voloch, J.F. Diagonal equations over function fields. Bol. Soc. Bras. Mat 16, 29–39 (1985). https://doi.org/10.1007/BF02584799
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DOI: https://doi.org/10.1007/BF02584799