Abstract
We study meromorphic functions in all ℂp or in a disc of ℂp. Using some properties of the valuation polygon notion, we show p-adic results perfectly analogous to those of Nevanlinna in the complex case.
As an application we prove the p-adic analogue of Malmquist-Yosida Theorem: Let m∈ℕ and R(x.y)∈ℂp(x,y). If the differential equation: (dy/dx)m=R(x,y), m∈ℕ, has a non rational meromorphic solution in all ℂp, then R(x,y) is a polynomial in y of degree ≤2m.
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Boutabaa, A. Theorie de nevanlinna p-adique. Manuscripta Math 67, 251–269 (1990). https://doi.org/10.1007/BF02568432
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DOI: https://doi.org/10.1007/BF02568432