Nevanlinna theory on the p-adic plane

Capi Corrales Rodrigáñez

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 2, page 135-147
  • ISSN: 0066-2216

Abstract

top
Let 𝕂 be a complete and algebraically closed non-Archimedean valued field. Following ideas of Marc Krasner and Philippe Robba, we define K-meromorphic functions from 𝕂 to 𝕂. We show that the Nevanlinna theory for functions of a single complex variable may be extended to those functions (and consequently to meromorphic functions).

How to cite

top

Capi Corrales Rodrigáñez. "Nevanlinna theory on the p-adic plane." Annales Polonici Mathematici 57.2 (1992): 135-147. <http://eudml.org/doc/262389>.

@article{CapiCorralesRodrigáñez1992,
abstract = {Let 𝕂 be a complete and algebraically closed non-Archimedean valued field. Following ideas of Marc Krasner and Philippe Robba, we define K-meromorphic functions from 𝕂 to 𝕂. We show that the Nevanlinna theory for functions of a single complex variable may be extended to those functions (and consequently to meromorphic functions).},
author = {Capi Corrales Rodrigáñez},
journal = {Annales Polonici Mathematici},
keywords = {K-meromorphic function; non-Archimedean valuation; Nevanlinna theory; -adic function theory; -meromorphic functions; Nevanlinna theory for functions},
language = {eng},
number = {2},
pages = {135-147},
title = {Nevanlinna theory on the p-adic plane},
url = {http://eudml.org/doc/262389},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Capi Corrales Rodrigáñez
TI - Nevanlinna theory on the p-adic plane
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 2
SP - 135
EP - 147
AB - Let 𝕂 be a complete and algebraically closed non-Archimedean valued field. Following ideas of Marc Krasner and Philippe Robba, we define K-meromorphic functions from 𝕂 to 𝕂. We show that the Nevanlinna theory for functions of a single complex variable may be extended to those functions (and consequently to meromorphic functions).
LA - eng
KW - K-meromorphic function; non-Archimedean valuation; Nevanlinna theory; -adic function theory; -meromorphic functions; Nevanlinna theory for functions
UR - http://eudml.org/doc/262389
ER -

References

top
  1. [1] W. W. Adams and E. G. Straus, Non-Archimedean analytic functions taking the same values at the same points, Illinois J. Math. 15 (1971), 418-424. Zbl0215.13202
  2. [2] I. N. Baker, The existence of fixpoints of entire functions, Math. Z. 73 (1960), 280-284. Zbl0129.29102
  3. [3] I. N. Baker and F. Gross, On factorizing entire functions, Proc. London Math. Soc. (3) 18 (1968), 69-76. Zbl0159.10002
  4. [4] F. Gross, Entire solutions to the functional equation a(b(z)) = a(g(z)) + c, J. Indian Math. Soc. 32 (1968), 199-206. Zbl0186.21403
  5. [5] F. Gross, On factorization of meromorphic functions, Trans. Amer. Math. Soc. 131 (1968), 215-221. Zbl0159.36702
  6. [6] F. Gross and C. F. Oswood, On fixed points of composite entire functions, J. London Math. Soc. (2) 28 (1983), 57-61. 
  7. [7] H. Hasse, Number Theory, Springer, 1980. 
  8. [8] W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford 1964. 
  9. [9] H. H. Khoai, On p-adic meromorphic functions, Duke Math. J. 50 (1983), 695-711. Zbl0544.30039
  10. [10] M. Krasner, Rapport sur le prolongement analytique dans les corps valués complets par la méthode des éléments analytiques quasi connexes, Bull. Soc. Math. France Mém. 39-40 (1974), 131-254. 
  11. [11] R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méro- morphes, Gauthier-Villars, Paris 1929. 
  12. [12] P. Robba, Fonctions analytiques sur les corps valués ultramétriques complets, Astérisque 10 (1973), 109-218. Zbl0289.12110
  13. [13] S. L. Segal, Nine Introductions in Complex Analysis, North-Holland Math. Stud. 53, 1981, 163-204. Zbl0482.30002
  14. [14] C.-C. Yang, Factorization Theory of Meromorphic Functions and Related Topics, Marcel Dekker, New York 1982. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.