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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation> be a Hecke–Maass form on a compact congruence arithmetic hyperbolic 3-manifold <i>X</i>, and let <i>Y</i> be a totally geodesic surface in <i>X</i> that is not necessarily closed. We obtain a power saving result over the local bound for the period of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation> along <i>Y</i>, by applying the method of arithmetic amplification developed by Iwaniec and Sarnak.</p>

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Bounds for the periods of eigenfunctions on arithmetic hyperbolic 3-manifolds over surfaces

  • 期刊论文

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  • 发表日期：

    2026年1月9日

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  • Jiaqi Hou

摘要

Let \(\psi \) ψ be a Hecke–Maass form on a compact congruence arithmetic hyperbolic 3-manifold X, and let Y be a totally geodesic surface in X that is not necessarily closed. We obtain a power saving result over the local bound for the period of \(\psi \) ψ along Y, by applying the method of arithmetic amplification developed by Iwaniec and Sarnak.