arXiv Open Access 2024

Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke-Maaß Cusp Forms on $\mathrm{SL}_2(\mathbb{Z}) \backslash \mathrm{SL}_2(\mathbb{R})$

Ankit Bisain Peter Humphries Andrei Mandelshtam Noah Walsh Xun Wang

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Abstrak

It is a folklore result in arithmetic quantum chaos that quantum unique ergodicity on the modular surface with an effective rate of convergence follows from subconvex bounds for certain triple product $L$-functions. The physical space manifestation of this result, namely the equidistribution of mass of Hecke-Maass cusp forms, was proven to follow from subconvexity by Watson, whereas the phase space manifestation of quantum unique ergodicity has only previously appeared in the literature for Eisenstein series via work of Jakobson. We detail the analogous phase space result for Hecke-Maass cusp forms. The proof relies on the Watson-Ichino triple product formula together with a careful analysis of certain archimedean integrals of Whittaker functions.

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math.NT

Penulis (5)

Ankit Bisain

Peter Humphries

Andrei Mandelshtam

Noah Walsh

Xun Wang

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APA MLA BibTeX

Bisain, A., Humphries, P., Mandelshtam, A., Walsh, N., Wang, X. (2024). Subconvexity Implies Effective Quantum Unique Ergodicity for Hecke-Maaß Cusp Forms on $\mathrm{SL}_2(\mathbb{Z}) \backslash \mathrm{SL}_2(\mathbb{R})$. https://arxiv.org/abs/2402.14050

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Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓