no. 2
An ultrametric Nevanlinna’s second main theorem for small functions of a special type
[Le theoréme de Nevanlinna ultramétrique pour petites fonctions]
Jurvanen, Henna1
1 Department of Physics and Mathematics University of Eastern Finland P.O.Box 111 Joensuu, FI-80101 FINLAND
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 : 10.5802/ambp.291
Classification : 12H99
Keywords: Ultrametric Nevanlinna theory, Second main theorem
Mot clés : Théorie de Nevanlinna ultramétrique
Jurvanen, Henna 1

1 Department of Physics and Mathematics University of Eastern Finland P.O.Box 111 Joensuu, FI-80101 FINLAND 
@article{AMBP_2010__17_2_425_0,
     author = {Jurvanen, Henna},
     title = {An ultrametric {Nevanlinna{\textquoteright}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},
     zbl = {1206.30062},
     mrnumber = {2778912},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.291/}
}
TY  - JOUR
AU  - Jurvanen, Henna
TI  - An ultrametric Nevanlinna’s second main theorem for small functions of a special type
JO  - Annales mathématiques Blaise Pascal
PY  - 2010
SP  - 425
EP  - 431
VL  - 17
IS  - 2
PB  - Annales mathématiques Blaise Pascal
UR  - http://www.numdam.org/articles/10.5802/ambp.291/
DO  - 10.5802/ambp.291
LA  - en
ID  - AMBP_2010__17_2_425_0
ER  - 
%0 Journal Article
%A Jurvanen, Henna
%T An ultrametric Nevanlinna’s second main theorem for small functions of a special type
%J Annales mathématiques Blaise Pascal
%D 2010
%P 425-431
%V 17
%N 2
%I Annales mathématiques Blaise Pascal
%U http://www.numdam.org/articles/10.5802/ambp.291/
%R 10.5802/ambp.291
%G en
%F 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/articles/10.5802/ambp.291/

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

[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 | Zbl

[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 | Zbl

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

[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 | DOI | MR | Zbl

Cité par Sources :