Meromorphic Functions on Annuli Sharing Few Small Functions with Truncated Multiplicities

Meromorphic Functions on Annuli Sharing Few Small Functions with Truncated Multiplicities 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 quangsd@hnue.edu.vn Huong Giang Ha hhgiang79@yahoo.com An Hai Tran trananhai@wru.vn 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Complex Analysis and Operator Theory Springer Journals

Meromorphic Functions on Annuli Sharing Few Small Functions with Truncated Multiplicities

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general; Operator Theory; Analysis
ISSN
1661-8254
eISSN
1661-8262
D.O.I.
10.1007/s11785-018-0808-3
Publisher site
See Article on Publisher Site

Abstract

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 quangsd@hnue.edu.vn Huong Giang Ha hhgiang79@yahoo.com An Hai Tran trananhai@wru.vn 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

Journal

Complex Analysis and Operator TheorySpringer Journals

Published: Jun 4, 2018

References

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