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Zbl 0593.30050
Feneyrol-Perrin, Yvette; Haddad, Labib
Un théorème de Mittag-Leffler pour les fonctions méromorphes sur un corps valué au sens de Krull. (A theorem of Mittag-Leffler for meromorphic functions on a field with valuation in the sense of Krull). (French)
[J] Compos. Math. 57, 249-269 (1986). ISSN 0010-437X; ISSN 1570-5846/e

Let K be a complete algebraically closed field whose valuation ring contains an infinite decreasing sequence of prime ideals having zero intersection. The authors continue previous studies on analytic functions on open subsets of K [the first author, Compos. Math. 49, 51-74 (1983; Zbl 0523.12022)] by proving the analogue of the Mittag-Leffler theorem. The remarkable feature is that conditions have to be imposed not only on the distribution of the poles but also on the principal parts that may be prescribed: the results had been announced in the authors' paper [C. R. Math. Acad. Sci., Soc. R. Can. 6, 199-204 (1984; Zbl 0546.12015)].
[F.Herrlich]

MSC 2000:: *30G06 Non-Archimedean function theory (one variable)
11S80 Other analytic theory of local fields

Keywords: field with valuation in the sense of Krull; Mittag-Leffler theorem

Citations: Zbl 0523.12022; Zbl 0546.12015

Cited in: Zbl 0593.30049

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