Duke Mathematical Journal

Subconvex equidistribution of cusp forms: Reduction to Eisenstein observables

Paul D. Nelson

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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.

Article information

Source
Duke Math. J., Volume 168, Number 9 (2019), 1665-1722.

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1560326499

Digital Object Identifier
doi:10.1215/00127094-2019-0005

Mathematical Reviews number (MathSciNet)
MR3961213

Subjects
Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 11F27: Theta series; Weil representation; theta correspondences 58J51: Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity

Keywords
subconvexity equidistribution quantum unique ergodicity L-functions automorphic forms Eisenstein series metaplectic group

Citation

Nelson, Paul D. Subconvex equidistribution of cusp forms: Reduction to Eisenstein observables. Duke Math. J. 168 (2019), no. 9, 1665--1722. doi:10.1215/00127094-2019-0005. https://projecteuclid.org/euclid.dmj/1560326499


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