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<p>We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2024_5203_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{GL}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>GL</mtext> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> Hecke–Maaß newforms over <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2024_5203_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Q}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Q</mi> </math></EquationSource> </InlineEquation> as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke–Maaß cusp forms to the modular surface dissipate as their Laplace eigenvalues grow.</p>

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New Variants of Arithmetic Quantum Ergodicity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月17日

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  • Peter Humphries,
  • Jesse Thorner

摘要

We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual \(\textrm{GL}_2\) GL 2 Hecke–Maaß newforms over \(\mathbb {Q}\) Q as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke–Maaß cusp forms to the modular surface dissipate as their Laplace eigenvalues grow.