Skip to main content Accessibility help
×
Home

On a new singular direction of meromorphic functions

  • Guo Hui (a1), Zheng Jian Hua (a2) and Tuen Wai Ng (a3)

Extract

In this paper, by using Ahlfors' theory of covering surfaces, we establish the existence of a new singular direction for a meromorphic functions f, namely a T direction for f, for which the Nevanlinna characteristic function T(r, f) is used as a comparison function.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On a new singular direction of meromorphic functions
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On a new singular direction of meromorphic functions
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On a new singular direction of meromorphic functions
      Available formats
      ×

Copyright

References

Hide All
[1]Chuang, C.T., Singular directions of meromorphic functions, (in Chinese) (Science Press, China, 1982).
[2]Gonchar, A.A., Havin, V.P. and Nikolski, N.K., Complex analysis I, Encyclopaedia of Mathematical Sciences 85 (Springer-Verlag, Berlin, 1997).
[3]Hayman, W.K., Meromorphic functions (Clarendon Press, Oxford, 1964).
[4]Hayman, W.K., ‘On the characteristic of functions meromorphic in the plane and of their integrals’, Proc. London Math. Soc. (3) 14 (1965), 93128.
[5]Julia, G., ‘Sur quelques proprietes nouvelles des functions entieres ou meromorphes’, Ann. Ecole Norm. Sup. 36 (1919), 93125; 37 (1920), 165–218.
[6]Offord, A.C., ‘Lacunary entire funcitons’, Math. Proc. Camb. Philos. Soc. 114 (1993), 6783.
[7]Ostrowski, A., ‘Ueber Folgen analytischer Funktionen und einige Verschearfungen des Picardschen Satzes’, Math. Zeit. 24 (1926), 215258.
[8]Tsuji, M., Potential theory in modern function theory (Maruzen Co. Ltd., Tokyo, 1959).
[9]Valiron, G., ‘Recherches sur le theoreme de M. Borel dans la theorie des functions meromorphes’, Acta Math. 52 (1928), 6792.
[10]Valiron, G., ‘Directions de Borel des fonctions meromorphes’, Mem. Sci. Math. Fasc. 89 (1938).
[11]Yang, L., ‘Borel directions of meromorphic functions in an angular domain’, Sci. Sinica (1979), 149163.
[12]Zhang, Q.D., ‘On Nevanlinna direction and Borel direction of meromorphic functions’, (in Chinese), Acta Math. Sinica 29 (1986), 550554.
[13]Zhang, Q.D. and Yang, L., ‘New singular direction of meromorphic functions’, (in Chinese), Sci. Sinica Ser. A 11 (1983), 982994.
[14]Zheng, J.H., ‘On transcendental meromorphic functions with radially distributed values’, Sci. Sinica Ser A (to appear).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

On a new singular direction of meromorphic functions

  • Guo Hui (a1), Zheng Jian Hua (a2) and Tuen Wai Ng (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed