caa a22 4500 606200991 CHVBK 20210128100946.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00025-014-0428-9 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0428-9 A Generalization of Brück's Conjecture for a Class of Entire Functions [Elektronische Daten] [Feng Lü, Hongxun Yi] In this paper, we study the uniqueness problem of entire functions sharing polynomials IM with their first derivative. As an application, we generalize Brück's conjecture from sharing value CM to sharing polynomial IM for a class of functions. In fact, we prove a result as follows: Let $${a({\not\equiv} 0)}$$ a ( ≢ 0 ) be a polynomial and $${n \geq 2}$$ n ≥ 2 be an integer, let f be a transcendental entire function, and let $${F = f^n}$$ F = f n . If F and F′ share a IM, then $${f(z) = Ae^{z/n},}$$ f ( z ) = A e z / n , where A is a nonzero constant. It extends some previous related theorems. Springer Basel, 2015 Differential equation nationallicence Nevanlinna theory nationallicence uniqueness nationallicence normal family nationallicence Lü Feng College of Science, China University of Petroleum, 266580, Qingdao, People's Republic of China aut Yi Hongxun Department of Mathematics, Shandong University, 250100, Jinan, People's Republic of China aut Results in Mathematics Springer Basel 68/1-2(2015-09-01), 157-169 1422-6383 68:1-2<157 2015 68 25 https://doi.org/10.1007/s00025-014-0428-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0428-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lü Feng College of Science, China University of Petroleum, 266580, Qingdao, People's Republic of China aut NATIONALLICENCE 700 1- Yi Hongxun Department of Mathematics, Shandong University, 250100, Jinan, People's Republic of China aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/1-2(2015-09-01), 157-169 1422-6383 68:1-2<157 2015 68 25