Soft bounds for local triple products and the subconvexity-QUE implication for ${\mathrm{GL}}_2$

Abstract

We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.

arXiv commentv2: 16 pages, minor revisions, modified title; to appear in Mathematika