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<p>We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke–Maass forms on quotients <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma \backslash {{({\mathbb H}^{(2)})}^{r}} \times {{({\mathbb H}^{(3)})}^{s}}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi mathvariant="normal">Γ</mi> <mi class="MJX-variant" mathvariant="normal">∖</mi> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>r</mi> </mrow> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>s</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. An argument by induction on dimension of the orbit allows us to rule out the limit measure giving positive mass to closed orbits of proper subgroups despite many returns of the Hecke correspondence to neighborhoods of the orbit.</p>

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Arithmetic quantum unique ergodicity for products of hyperbolic 2- and 3-spaces

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Zvi Shem-Tov,
  • Lior Silberman

摘要

We prove the arithmetic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke–Maass forms on quotients \(\Gamma \backslash {{({\mathbb H}^{(2)})}^{r}} \times {{({\mathbb H}^{(3)})}^{s}}\) Γ ∖ ( H ( 2 ) ) r × ( H ( 3 ) ) s . An argument by induction on dimension of the orbit allows us to rule out the limit measure giving positive mass to closed orbits of proper subgroups despite many returns of the Hecke correspondence to neighborhoods of the orbit.