Meromorphic functions of infinite order in the angular domain

Jun-Fan Chen

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1103-1112
  • ISSN: 2391-5455

Abstract

top
We investigate the value distribution of meromorphic functions in the angular domain. In particular, we show a close relationship between radially distributed values and Borel directions of transcendental meromorphic functions of infinite order in some angular domains.

How to cite

top

Jun-Fan Chen. "Meromorphic functions of infinite order in the angular domain." Open Mathematics 10.3 (2012): 1103-1112. <http://eudml.org/doc/269382>.

@article{Jun2012,
abstract = {We investigate the value distribution of meromorphic functions in the angular domain. In particular, we show a close relationship between radially distributed values and Borel directions of transcendental meromorphic functions of infinite order in some angular domains.},
author = {Jun-Fan Chen},
journal = {Open Mathematics},
keywords = {Meromorphic function; Infinite order; Borel direction; Radial distribution; Angular domain; meromorphic function; infinite order; radial distribution; angular domain},
language = {eng},
number = {3},
pages = {1103-1112},
title = {Meromorphic functions of infinite order in the angular domain},
url = {http://eudml.org/doc/269382},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Jun-Fan Chen
TI - Meromorphic functions of infinite order in the angular domain
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1103
EP - 1112
AB - We investigate the value distribution of meromorphic functions in the angular domain. In particular, we show a close relationship between radially distributed values and Borel directions of transcendental meromorphic functions of infinite order in some angular domains.
LA - eng
KW - Meromorphic function; Infinite order; Borel direction; Radial distribution; Angular domain; meromorphic function; infinite order; radial distribution; angular domain
UR - http://eudml.org/doc/269382
ER -

References

top
  1. [1] Chen S.-J., Lin W.-C., Chen J.-F., On the growth of meromorphic functions with a radially distributed value, Indian J. Pure Appl. Math., 2011, 42(1), 53–70 http://dx.doi.org/10.1007/s13226-011-0004-x Zbl1306.30013
  2. [2] Chuang C., Sur les fonctions-types, Sci. Sinica, 1961, 10, 171–181 
  3. [3] Fang M., Zalcman L., On the value distribution of f + a(f′)n, Sci. China Ser. A, 2008, 51(7), 1196–1202 http://dx.doi.org/10.1007/s11425-008-0022-2 Zbl1158.30020
  4. [4] Goldberg A.A., Ostrovskii I.V., The Distribution of Values of Meromorphic Functions, Nauka, Moscow, 1970 (in Russian) 
  5. [5] Hayman W.K., Picard values of meromorphic functions and their derivatives, Ann. of Math., 1959, 70(1), 9–42 http://dx.doi.org/10.2307/1969890 Zbl0088.28505
  6. [6] Hayman W.K., Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964 
  7. [7] Hiong K.L., Sur les fonctions entières et les fonctions méromorphes d’ordre infini, J. Math. Pures Appl., 1935, 14, 233–308 Zbl0012.26401
  8. [8] Nevanlinna R., Über die Eigenschaften meromorpher Funktionen in einem Winkelraum, Acta Societatis Scientiarum Fennicae, 1925, 50, #12 Zbl51.0257.02
  9. [9] Valiron G., Sur les directions de Borel des fonctions méromorphes d’ordre infini, C. R. Acad. Sci. Paris Sér. I Math., 1938, 206, 575–577 Zbl0018.07304
  10. [10] Yang C.-C., Yi H.-X., Uniqueness Theory of Meromorphic Functions, Math. Appl., 557, Kluwer, Dordrecht, 2003 
  11. [11] Yang L., Some recent results and problems in the theory of value distribution, In: Proceedings Symposium on Value Distribution Theory in Several Complex Variables, Notre Dame, April 28–29, 1990, Notre Dame Math. Lectures, 12, University of Notre Dame, Notre Dame, 1992, 157–171 
  12. [12] Yang L., Value Distribution Theory, Springer, Berlin, 1993 Zbl0790.30018
  13. [13] Yang L., Yang C.C., Angular distribution of values of ff′, Sci. China Ser. A, 1994, 37(3), 284–294 Zbl0804.30024
  14. [14] Ye Y.S., A Picard type theorem and Bloch law, Chinese Ann. Math. Ser. B, 1994, 15(1), 75–80 
  15. [15] Zheng J., On transcendental meromorphic functions with radially distributed values, Sci. China Ser. A, 2004, 47(3), 401–416 http://dx.doi.org/10.1360/02ys0210 
  16. [16] Zhuang Q.-T., Hu Z.-J., Common Borel directions of a meromorphic function of infinite order and its differential polynomial, Chinese Sci. Bull., 1992, 37(7), 541–547 Zbl0754.30026

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.