# An ultrametric Nevanlinna’s second main theorem for small functions of a special type

Henna Jurvanen^{[1]}

- [1] Department of Physics and Mathematics University of Eastern Finland P.O.Box 111 Joensuu, FI-80101 FINLAND

Annales mathématiques Blaise Pascal (2010)

- Volume: 17, Issue: 2, page 425-431
- ISSN: 1259-1734

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topJurvanen, Henna. "An ultrametric Nevanlinna’s second main theorem for small functions of a special type." Annales mathématiques Blaise Pascal 17.2 (2010): 425-431. <http://eudml.org/doc/116360>.

@article{Jurvanen2010,

abstract = {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.},

affiliation = {Department of Physics and Mathematics University of Eastern Finland P.O.Box 111 Joensuu, FI-80101 FINLAND},

author = {Jurvanen, Henna},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Ultrametric Nevanlinna theory; Second main theorem; ultrametric Nevanlinna theory; second main theorem},

language = {eng},

month = {7},

number = {2},

pages = {425-431},

publisher = {Annales mathématiques Blaise Pascal},

title = {An ultrametric Nevanlinna’s second main theorem for small functions of a special type},

url = {http://eudml.org/doc/116360},

volume = {17},

year = {2010},

}

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

DA - 2010/7//

PB - Annales mathématiques Blaise Pascal

VL - 17

IS - 2

SP - 425

EP - 431

AB - 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.

LA - eng

KW - Ultrametric Nevanlinna theory; Second main theorem; ultrametric Nevanlinna theory; second main theorem

UR - http://eudml.org/doc/116360

ER -

## References

top- A. Boutabaa, Théorie de Nevanlinna p-adique, Manuscripta Math. 67 (1990), 251-269 Zbl0697.30047MR1046988
- A. Boutabaa, A. Escassut, An improvement of the p-adic Nevanlinna theory and application to meromorphic functions, Lecture Notes in Pure and Appl. Math. 207 (1999), 29-38 Zbl0937.30028MR1702045
- A. Boutabaa, A. Escassut, Applications of the p-adic Nevanlinna Theory, Lecture Notes in Pure and Appl. Math. 222 (2001), 49-61 Zbl1005.30036MR1838281
- A. Escassut, Analytic Elements in p-adic Analysis,, (1995), World Scientific, Singapore Zbl0933.30030MR1370442
- A. Escassut, p-adic value distribution, Some topics on value distribution and differentiability in complex and p-adic analysis, (2008), Science Press, Beijing Zbl1233.30005
- K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), 225-294 Zbl1203.30035MR2096455

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