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Quantum Unique Ergodicity for half-integral weight automorphic forms

Lester, Stephen and Radziwiłł, Maksym (2016) Quantum Unique Ergodicity for half-integral weight automorphic forms. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20180613-084101704

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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 QUE for both half-integral weight holomorphic Hecke cusp forms for Γ_0(4) lying in Kohnen's plus subspace and for half-integral weight Hecke Maaβ cusp forms for Γ_0(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 equidistribute with respect to hyperbolic measure on Γ_0(4)∖H as the weight tends to infinity.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1606.04119arXivDiscussion Paper
ORCID:
AuthorORCID
Lester, Stephen0000-0003-1977-9205
Alternate Title:Quantum Unique Ergodicity for half-integral weight forms
Additional Information:This paper is an outgrowth of our joint work with Kaisa Matomäki [22] and we are especially thankful to her for her numerous ideas and suggestions. We are also very grateful to Zeév Rudnick and Peter Sarnak for many conversations related to this project and for their encouragement. We would also like to thank Kannan Soundararajan for many discussions on moments and Valentin Blomer for very useful pointers to the literature on Whittaker functions.
Classification Code:2010 Mathematics Subject Classification: 11F37, 11F30 (primary), 11M41 (secondary)
Record Number:CaltechAUTHORS:20180613-084101704
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180613-084101704
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87048
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Jun 2018 16:19
Last Modified:05 Nov 2019 17:30

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