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<p>Given a large, square-free, smooth conductor, we establish the non-vanishing of the central values for at least <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1032_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(35.9\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>35.9</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the primitive Dirichlet <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1032_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(L\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>L</mi> </math></EquationSource> </InlineEquation>-functions.</p>

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Non-vanishing of Dirichlet \(L\)-functions with smooth conductors

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Sun-Kai Leung

摘要

Given a large, square-free, smooth conductor, we establish the non-vanishing of the central values for at least \(35.9\%\) 35.9 % of the primitive Dirichlet \(L\) L -functions.