• 대한수학회보
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• 제51권1호
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• pp.83-98
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• 2014

During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

• 대한수학회보
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• 제55권1호
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• pp.205-226
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• 2018

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.