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Meromorphic Functions on Annuli Sharing Few Small Functions with Truncated Multiplicities

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Abstract

In this paper, we show that two admissible meromorphic functions on an annulus must coincide to each other if they share \(q\ (q\ge 5)\) 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.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.04-2018.01.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Duc Quang Si

  2. Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam

    Duc Quang Si

  3. Faculty of Fundamental Sciences, Electric Power University, 235-Hoang Quoc Viet, Tu Liem, Hanoi, Vietnam

    Huong Giang Ha

  4. Division of Mathematics, Banking Academy, 12-Chua Boc, Dong Da, Hanoi, Vietnam

    An Hai Tran

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  1. Duc Quang Si
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  2. Huong Giang Ha
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  3. An Hai Tran
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Correspondence to Duc Quang Si.

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Communicated by Daniel Aron Alpay.

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Si, D.Q., Ha, H.G. & Tran, A.H. Meromorphic Functions on Annuli Sharing Few Small Functions with Truncated Multiplicities. Complex Anal. Oper. Theory 13, 1693–1711 (2019). https://doi.org/10.1007/s11785-018-0808-3

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  • DOI: https://doi.org/10.1007/s11785-018-0808-3

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