Valuations on meromorphic functions of bounded type

Nakai, Mitsuru

doi:10.1090/S0002-9947-1988-0957069-4

Valuations on meromorphic functions of bounded type
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by Mitsuru Nakai

Trans. Amer. Math. Soc. 309 (1988), 231-252

DOI: https://doi.org/10.1090/S0002-9947-1988-0957069-4

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Abstract:

The primary purpose of this paper is to show that every valuation on the field of meromorphic functions of bounded type on a finitely sheeted unlimited covering Riemann surface is a point valuation if and only if the same is true on its base Riemann surface. The result is then applied to concrete examples and some related results are obtained.

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