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On the Cardinality of Unique Range Sets with Weight One

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Ukrainian Mathematical Journal Aims and scope

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Two meromorphic functions f and g are said to share a set S ⊂ ℂ∪ {∞} with weight l ∈ ℕ∪{0}∪{∞} if Ef (S, l) = Eg(S, l), where

$$ {E}_f\left(S,l\right)=\underset{\alpha \in S}{\cup}\left\{\left(z,t\right)\in \mathrm{\mathbb{C}}\times \left.\mathrm{\mathbb{N}}\right|f(z)=a\kern0.5em \mathrm{with}\kern0.5em \mathrm{multiplicity}\kern1em p\right\}, $$

provided that t = p for p ≤ l and t = p + 1 for p > l. We improve and supplement the result by L.W. Liao and C. C. Yang [Indian J. Pure Appl. Math., 31, No. 4, 431–440 (2000)] by showing that there exists a finite set S with 13 elements such that Ef (S, 1) = Eg(S, 1) implies that f ≡ g.

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Authors and Affiliations

  1. Ramakrishna Mission Vivekananda Centenary College, Khardaha, West Bengal, India

    B. Chakraborty

  2. Jadavpur University, Kolkata, West Bengal, India

    S. Chakraborty

Authors
  1. B. Chakraborty
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  2. S. Chakraborty
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Correspondence to B. Chakraborty.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 7, pp. 997–1005, July, 2020. Ukrainian DOI: 10.37863/umzh.v72i7.6022.

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Chakraborty, B., Chakraborty, S. On the Cardinality of Unique Range Sets with Weight One. Ukr Math J 72, 1164–1174 (2020). https://doi.org/10.1007/s11253-020-01849-z

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  • DOI: https://doi.org/10.1007/s11253-020-01849-z

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