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<p>We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="39_2025_714_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>L</mi> </math></EquationSource> <EquationSource Format="TEX">$L$</EquationSource> </InlineEquation>-functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.</p>

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Local Integral Transforms and Global Spectral Decomposition

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月10日

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  • Valentin Blomer,
  • Subhajit Jana,
  • Paul D. Nelson

摘要

We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic L $L$ -functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.