On the cardinality of a reduced unique range set
UDC 517.5Two meromorphic functions are said to share a set $S\subset \mathbb{C}\cup\{\infty\}$ ignoring multiplicities (IM) if $S$ has the same pre-images under both functions. If any two nonconstant meromorphic functions, sharing a set IM, are identical, then the set is called a “reduced unique ran...
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| Datum: | 2020 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/594 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5Two meromorphic functions are said to share a set $S\subset \mathbb{C}\cup\{\infty\}$ ignoring multiplicities (IM) if $S$ has the same pre-images under both functions. If any two nonconstant meromorphic functions, sharing a set IM, are identical, then the set is called a “reduced unique range set for meromorphic functions'' (in short, RURSM or URSM-IM).
From the existing literature, it is known that there exists a RURSM with seventeen elements. In this article, we reduced the cardinality of an existing RURSM and established that there exists a RURSM with fifteen elements. Our result gives an affirmative answer to the question of L. Z. Yang (Int. Soc. Anal., Appl., and Comput., 7, 551–564 (2000)). |
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| DOI: | 10.37863/umzh.v72i11.594 |