Meromorphic solutions of some q-difference equations
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We consider meromorphic solutions of $q$-difference equations of the form [수식]=a_(n+1)(z), where a_0(z), ...,a_(n+1)(z) are meromorphic functions, a_0(z)a_n(z)[기호] 0 and q∈C such that 0<|q|≤ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0<|q|<1 and n=2. Some growth estimates for meromorphic solutions are also given in the cases 0<|q|<1 and |q|=1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q|=1.
Abstract
We consider meromorphic solutions of $q$-difference equations of the form [수식]=a_(n+1)(z), where a_0(z), ...,a_(n+1)(z) are meromorphic functions, a_0(z)a_n(z)[기호] 0 and q∈C such that 0<|q|≤ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0<|q|<1 and n=2. Some growth estimates for meromorphic solutions are also given in the cases 0<|q|<1 and |q|=1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q|=1.
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