Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 9 (2019), 1665-1722.
Subconvex equidistribution of cusp forms: Reduction to Eisenstein observables
Let traverse a sequence of cuspidal automorphic representations of with large prime level, unramified central character, and bounded infinity type. For , let denote the assertion that subconvexity holds for -twists of the adjoint -function of , with polynomial dependence upon the conductor of the twist. We show that implies .
In geometric terms, corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term, , to the special case in which the relevant sequence of measures is tested against an Eisenstein series.
Duke Math. J., Volume 168, Number 9 (2019), 1665-1722.
Received: 14 February 2017
Revised: 10 January 2019
First available in Project Euclid: 12 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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