Displaying similar documents to “The L-function L3(s, ...) is entire.”

Differential analogues of the Brück conjecture

Xiao-Guang Qi, Lian-Zhong Yang (2011)

Annales Polonici Mathematici

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We give some growth properties for solutions of linear complex differential equations which are closely related to the Brück Conjecture. We also prove that the Brück Conjecture holds when certain proximity functions are relatively small.

Entire functions that share a function with their first and second derivatives

Feng Lü, Junfeng Xu (2012)

Annales Polonici Mathematici

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Applying the normal family theory and the theory of complex differential equations, we obtain a uniqueness theorem for entire functions that share a function with their first and second derivative, which generalizes several related results of G. Jank, E. Mues & L. Volkmann (1986), C. M. Chang & M. L. Fang (2002) and I. Lahiri & G. K. Ghosh (2009).

Entire functions that share values or small functions with their derivatives

Sheng Li, Zongsheng Gao, Jilong Zhang (2012)

Annales Polonici Mathematici

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We investigate the uniqueness of entire functions sharing values or small functions with their derivatives. One of our results gives a necessary condition on the Nevanlinna deficiency of the entire function f sharing one nonzero finite value CM with its derivative f'. Some applications of this result are provided. Finally, we prove some further results on small function sharing.