An ultrametric Nevanlinna’s second main theorem for small functions of a special type  [ Le theoréme de Nevanlinna ultramétrique pour petites fonctions ]
Annales Mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 425-431.

En théorie de Nevanlinna ultramétrique, le second théorème fondamental de Nevanlinna pour des petites fonctions a seulement été établi pour trois petites fonctions. Dans cet article, on montre un second théorème fondamental pour q petites fonctions d’un certain type quand la caractéristique résiduelle du corps est zero.

In ultrametric Nevanlinna theory, the Nevanlinna’s second main theorem for small functions has only been proved in the case of at most three small functions. In this paper, we prove a second main theorem for q small functions of a special type when the residue characteristic of the field is zero.

DOI : https://doi.org/10.5802/ambp.291
Classification : 12H99
Mots clés : Théorie de Nevanlinna ultramétrique
@article{AMBP_2010__17_2_425_0,
     author = {Jurvanen, Henna},
     title = {An ultrametric Nevanlinna's second main theorem for small functions of a special type},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {425--431},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {17},
     number = {2},
     year = {2010},
     doi = {10.5802/ambp.291},
     mrnumber = {2778912},
     zbl = {1206.30062},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2010__17_2_425_0/}
}
Jurvanen, Henna. An ultrametric Nevanlinna’s second main theorem for small functions of a special type. Annales Mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 425-431. doi : 10.5802/ambp.291. http://www.numdam.org/item/AMBP_2010__17_2_425_0/

[1] Boutabaa, A. Théorie de Nevanlinna p-adique, Manuscripta Math., Volume 67 (1990), pp. 251-269 | Article | EuDML 155499 | MR 1046988 | Zbl 0697.30047

[2] Boutabaa, A.; Escassut, A. An improvement of the p-adic Nevanlinna theory and application to meromorphic functions, Lecture Notes in Pure and Appl. Math., Volume 207 (1999), pp. 29-38 | MR 1702045 | Zbl 0937.30028

[3] Boutabaa, A.; Escassut, A. Applications of the p-adic Nevanlinna Theory, Lecture Notes in Pure and Appl. Math., Volume 222 (2001), pp. 49-61 | MR 1838281 | Zbl 1005.30036

[4] Escassut, A. Analytic Elements in p-adic Analysis,, World Scientific, Singapore, 1995 | MR 1370442 | Zbl 0933.30030

[5] Escassut, A. p-adic value distribution, Some topics on value distribution and differentiability in complex and p-adic analysis, Science Press, Beijing, 2008

[6] Yamanoi, K. The second main theorem for small functions and related problems, Acta Math., Volume 192 (2004), pp. 225-294 | Article | MR 2096455 | Zbl 1203.30035