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

Abstract

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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.

How to cite

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Jurvanen, 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

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  1. A. Boutabaa, Théorie de Nevanlinna p-adique, Manuscripta Math. 67 (1990), 251-269 Zbl0697.30047MR1046988
  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. 207 (1999), 29-38 Zbl0937.30028MR1702045
  3. A. Boutabaa, A. Escassut, Applications of the p-adic Nevanlinna Theory, Lecture Notes in Pure and Appl. Math. 222 (2001), 49-61 Zbl1005.30036MR1838281
  4. A. Escassut, Analytic Elements in p-adic Analysis,, (1995), World Scientific, Singapore Zbl0933.30030MR1370442
  5. 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
  6. K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), 225-294 Zbl1203.30035MR2096455

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