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<p>We propose (and prove under some restrictions) that the square class of the central value of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1349_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>-function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is parallel to the appearance of metaplectic groups in quantization. In the course of the proof we also establish a topological analogue of this statement, concerning Reidemeister torsion of 3-manifolds.</p>

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Symplectic \(L\)-functions and symplectic Reidemeister torsion (mod squares)

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Amina Abdurrahman,
  • Akshay Venkatesh

摘要

We propose (and prove under some restrictions) that the square class of the central value of the L $L$ -function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is parallel to the appearance of metaplectic groups in quantization. In the course of the proof we also establish a topological analogue of this statement, concerning Reidemeister torsion of 3-manifolds.