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<p>In this paper, we investigate the sign-change problem for Fourier coefficients of two and three newforms. One of our main ingredients is determine the Rankin-Selberg <i>L</i>-functions corresponding to the configurations <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1101_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {GL}_4\times \text {GL}_4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>GL</mtext> <mn>4</mn> </msub> <mo>×</mo> <msub> <mtext>GL</mtext> <mn>4</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1101_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {GL}_8\times \text {GL}_8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>GL</mtext> <mn>8</mn> </msub> <mo>×</mo> <msub> <mtext>GL</mtext> <mn>8</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> in the level aspect concluding the local factors at ramified and unramified places, as well as the first or second moment related to these <i>L</i>-functions in the level aspect. We improve and generalize previous results.</p>

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Sign changes in short intervals related to Rankin-Selberg L-functions in the level aspect

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • Fei Hou,
  • Yishen Wang,
  • Junjie Pan

摘要

In this paper, we investigate the sign-change problem for Fourier coefficients of two and three newforms. One of our main ingredients is determine the Rankin-Selberg L-functions corresponding to the configurations \(\text {GL}_4\times \text {GL}_4\) GL 4 × GL 4 and \(\text {GL}_8\times \text {GL}_8\) GL 8 × GL 8 in the level aspect concluding the local factors at ramified and unramified places, as well as the first or second moment related to these L-functions in the level aspect. We improve and generalize previous results.