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Abstract <p> Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb K\)</EquationSource> </InlineEquation> be an algebraically closed field of characteristic zero, complete with respect to a non-Archimedean absolute value. We first give a sufficient condition for a finite set <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(S\subset {\mathbb K}\)</EquationSource> </InlineEquation> such that if <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(g \)</EquationSource> </InlineEquation> share <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(S\)</EquationSource> </InlineEquation> ignoring multiplicity, then <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\( f=g.\)</EquationSource> </InlineEquation> As consequences, we obtain a new class of unique range sets for non-Archimedean meromorphic functions ignoring multiplicity with <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1110_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(14\)</EquationSource> </InlineEquation> elements. Our result improves and generalizes some previous results of Banerjee-Maity in [<CitationRef CitationID="CR5">5</CitationRef>], Hu-Yang in [<CitationRef CitationID="CR10">10</CitationRef>] and Escassut-Haddad-Vidal in [<CitationRef CitationID="CR3">3</CitationRef>]. </p>

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URSIM for Meromorphic Functions in a non-Archimedean Field

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Vu Hoai An,
  • Phommavong Chanthaphone

摘要

Abstract

Let \(\mathbb K\) be an algebraically closed field of characteristic zero, complete with respect to a non-Archimedean absolute value. We first give a sufficient condition for a finite set \(S\subset {\mathbb K}\) such that if \(f\) and \(g \) share \(S\) ignoring multiplicity, then \( f=g.\) As consequences, we obtain a new class of unique range sets for non-Archimedean meromorphic functions ignoring multiplicity with \(14\) elements. Our result improves and generalizes some previous results of Banerjee-Maity in [5], Hu-Yang in [10] and Escassut-Haddad-Vidal in [3].