no. 2
An ultrametric Nevanlinna’s second main theorem for small functions of a special type
Henna Jurvanen1
1 Department of Physics and Mathematics University of Eastern Finland P.O.Box 111 Joensuu, FI-80101 FINLAND
Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 2, pp. 425-431.

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.

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.

DOI: 10.5802/ambp.291
Classification: 12H99
Keywords: Ultrametric Nevanlinna theory, Second main theorem
Mots-clés : Théorie de Nevanlinna ultramétrique

Henna Jurvanen 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 = {Henna Jurvanen},
     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},
     mrnumber = {2778912},
     zbl = {1206.30062},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.291/}
}
TY  - JOUR
AU  - Henna Jurvanen
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  - https://ambp.centre-mersenne.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 Henna Jurvanen
%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 https://ambp.centre-mersenne.org/articles/10.5802/ambp.291/
%R 10.5802/ambp.291
%G en
%F AMBP_2010__17_2_425_0
Henna Jurvanen. An ultrametric Nevanlinna’s second main theorem for small functions of a special type. Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 2, pp. 425-431. doi : 10.5802/ambp.291. https://ambp.centre-mersenne.org/articles/10.5802/ambp.291/

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

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

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

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

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

Cited by Sources: