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<p>We prove that for any prime <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_836_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(p&gt; 3\)</EquationSource> </InlineEquation> and any extension degree <i>m</i> of the prime field <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_836_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_{p}\)</EquationSource> </InlineEquation>, the Kloosterman sums <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_836_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal{K}_{p^{m}}(u)\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12095_2025_836_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(u \in \mathbb {F}^{*}_{p}\)</EquationSource> </InlineEquation> are distinct.</p>

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Distinctness of the lifted kloosterman sums on the prime field \(\mathbb {F}_p,\; p> 3\)

  • 期刊论文

  • 发表日期：

    2025年9月10日

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  • Lyubomir Borissov,
  • Yuri Borissov

摘要

We prove that for any prime \(p> 3\) and any extension degree m of the prime field \(\mathbb {F}_{p}\) , the Kloosterman sums \(\mathcal{K}_{p^{m}}(u)\) with \(u \in \mathbb {F}^{*}_{p}\) are distinct.