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Theorie de Nevanlinna p-adique. (p-adic Nevanlinna theory). (French) Zbl 0697.30047
Nevanlinna theory for meromorphic functions on \({\mathbb{C}}_ p\) has been studied by Hà Huy Khoai. In the present paper the two fundamental theorems are proven for all meromorphic functions. As a consequence a p- adic analogue of the Malmquist-Yosida theorem is found. The proofs are similar to the complex case (and easier). There are no examples to show that the second inequality \(\sum \delta (\alpha)\leq 2\) is best possible.
Reviewer: M.van der Put

30G06 Non-Archimedean function theory
Full Text: DOI EuDML
[1] Amice, Y.,Les nombres p-adiques, Paris, P.U.F., 1975 · Zbl 0313.12104
[2] Hà Huy Khoai,On p-adic meromorphic functions, Duke Math. J., vol. 50, no 3, 695–711, (1983). · Zbl 0544.30039 · doi:10.1215/S0012-7094-83-05033-0
[3] Malmquist, J.,Sur les fonctions à un nombre fini de branches définies par les équations différentielles du premier ordre, Acta Math. 36, 297–343, (1913) · JFM 44.0384.01 · doi:10.1007/BF02422385
[4] Nevanlinna, R.,Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Paris, 1929 · JFM 55.0773.03
[5] Robba, P.,Fonctions analytiques sur les corps valués ultramétriques complets, Astérisque no 10, 109–218, (1973), (Paris Soc. Math. Fr.)
[6] Valiron, G.,Sur la dérivée des fonctions algébroides, Bull. Soc. Math. de France no 49, 17–39, (1931). · JFM 57.0371.01
[7] Yosida, K.,A generalization of Malmquist’s theorem, Japan J. Math. 9, 253–256, (1932) · Zbl 0007.12002
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