Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0808-3 and Operator Theory Meromorphic Functions on Annuli Sharing Few Small Functions with Truncated Multiplicities 1,2 3 Duc Quang Si · Huong Giang Ha · An Hai Tran Received: 3 February 2018 / Accepted: 28 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this paper, we show that two admissible meromorphic functions on an annulus must coincide to each other if they share q (q ≥ 5) distinct small functions regardless of multiplicity. We also show that such two meromorphic functions must be linked by a quasi-Möbius transformation if they share four distinct small functions with multiplicities truncated by a certain level. Moreover, in our result, all intersection points of such meromorphic functions with small functions do not need to be counted if their multiplicities are bigger than a certain number. Keywords Meromorphic function · Nevanlinna theory · The annulus Mathematics Subject Classiﬁcation Primary 30D35 Communicated by Daniel Aron Alpay. B Duc Quang Si firstname.lastname@example.org Huong Giang Ha email@example.com An Hai Tran firstname.lastname@example.org Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy, Cau Giay, Hanoi, Vietnam Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan
Complex Analysis and Operator Theory – Springer Journals
Published: Jun 4, 2018
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