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math.CV2006★ 17 cited
Difference independence of the Riemann zeta function
Yik-Man Chiang, Shaoji Feng
It is proved that the Riemann zeta function does not satisfy any nontrivial algebraic difference equation whose coefficients are meromorphic functions with Nevanlinna character…
math.CV2006
On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions
Yik-Man Chiang, Shaoji Feng
A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and Korhonen \cite{AHH}, \cite {HK-2} that a connection exists between discrete Painlevé equations and (fi…
math.CV2006
On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane
Y. M. Chiang, S. J. Feng
We investigate the growth of the Nevanlinna Characteristic of f(z+η) for a fixed ηin this paper. In particular, we obtain a precise asymptotic relation between T(r,f(z+η) and T(r,f…