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1 February 2020 Quantum unique ergodicity for half-integral weight automorphic forms
Stephen Lester, Maksym Radziwiłł
Duke Math. J. 169(2): 279-351 (1 February 2020). DOI: 10.1215/00127094-2019-0040

Abstract

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.

Citation

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Stephen Lester. Maksym Radziwiłł. "Quantum unique ergodicity for half-integral weight automorphic forms." Duke Math. J. 169 (2) 279 - 351, 1 February 2020. https://doi.org/10.1215/00127094-2019-0040

Information

Received: 4 September 2017; Revised: 11 June 2019; Published: 1 February 2020
First available in Project Euclid: 29 January 2020

zbMATH: 07180378
MathSciNet: MR4057145
Digital Object Identifier: 10.1215/00127094-2019-0040

Subjects:
Primary: 11F37
Secondary: 11F30, 11M41

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 2 • 1 February 2020
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