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Quantum unique ergodicity for half-integral weight automorphic forms

Research output: Contribution to journalArticlepeer-review

Stephen Lester, Maksym Radziwill

Original languageEnglish
Pages (from-to)279 - 351
JournalDuke mathematical journal
Issue number2
Accepted/In press10 Jul 2019
Published1 Feb 2020


  • automorphic_revisions

    automorphic_revisions_8.pdf, 596 KB, application/pdf

    Uploaded date:05 Mar 2021

    Version:Accepted author manuscript

King's Authors


We investigate the analogue of the quantum unique ergodicity (QUE) conjecture for half-integral weight automorphic forms. Assuming the generalized Riemann hypothesis (GRH), we establish both QUE for half-integral weight Hecke Maaß cusp forms for Γ0(4) lying in Kohnen’s plus subspace and mass equidistribution for half-integral weight holomorphic Hecke cusp forms for Γ0(4) lying in Kohnen’s plus subspace. By combining the former result along with an argument of Rudnick, it follows that under GRH the zeros of these holomorphic Hecke cusp forms equidistribute with respect to hyperbolic measure on
Γ0(4)\H as the weight tends to infinity.

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