Skip to main content
×
Home
    • Aa
    • Aa

Nevanlinna theory for the $q$-difference operator and meromorphic solutions of $q$-difference equations

  • D. C. Barnett (a1), R. G. Halburd (a1), W. Morgan (a1) and R. J. Korhonen (a2)
Abstract

It is shown that, if $f$ is a meromorphic function of order zero and $q\in\mathbb{C}$, then

\begin{equation} \label{abstid} m\bigg(r,\frac{f(qz)}{f(z)}\bigg)=o(T(r,f)) \tag{\ddag} \end{equation}

for all $r$ on a set of logarithmic density $1$. The remainder of the paper consists of applications of identity \eqref{abstid} to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of $q$-difference equations. The results obtained include $q$-shift analogues of the second main theorem of Nevanlinna theory, Picard's theorem, and Clunie and Mohon'ko lemmas.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 10 *
Loading metrics...

Abstract views

Total abstract views: 87 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.