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15 June 2019 Subconvex equidistribution of cusp forms: Reduction to Eisenstein observables
Paul D. Nelson
Duke Math. J. 168(9): 1665-1722 (15 June 2019). DOI: 10.1215/00127094-2019-0005

Abstract

Let π traverse a sequence of cuspidal automorphic representations of GL2 with large prime level, unramified central character, and bounded infinity type. For G{GL1,PGL2}, let H(G) denote the assertion that subconvexity holds for G-twists of the adjoint L-function of π, with polynomial dependence upon the conductor of the twist. We show that H(GL1) implies H(PGL2).

In geometric terms, H(PGL2) corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term, H(GL1), to the special case in which the relevant sequence of measures is tested against an Eisenstein series.

Citation

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Paul D. Nelson. "Subconvex equidistribution of cusp forms: Reduction to Eisenstein observables." Duke Math. J. 168 (9) 1665 - 1722, 15 June 2019. https://doi.org/10.1215/00127094-2019-0005

Information

Received: 14 February 2017; Revised: 10 January 2019; Published: 15 June 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07097312
MathSciNet: MR3961213
Digital Object Identifier: 10.1215/00127094-2019-0005

Subjects:
Primary: 11F70
Secondary: 11F27, 58J51

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 9 • 15 June 2019
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