A note on the Bruck conjecture

作者：Li Sheng^*; Gao Zongsheng

来源：Archiv der Mathematik, 2010, 95(3): 257-268.

DOI：10.1007/s00013-010-0165-6

• Bruck conjecture
• Derivative
• Shift
• Difference
• Shared value

In this paper, we firstly consider the Bruck conjecture itself and show that it holds exactly for the entire function f(z) = 1/c (Ae(c/z) - a)+ a, , where A, a, c are nonzero constants. Then we give a necessary and sufficient condition that f(z) and f '(z) share a finite value a CM for some special cases. Finally, we investigate two analogues of the Bruck conjecture including the difference analogue of the Bruck conjecture raised by Liu and Yang (Arch. Math. 92, 270-278 (2009)) and the shifted analogue of the Bruck conjecture raised by Heittokangas et al. (J. Math. Anal. Appl. 355, 352-363 (2009)). And we give some necessary conditions when f(z) shares a finite value a CM with its difference operators or shifts.

• 出版日期2010-9
• 单位北京航空航天大学