Subconvexity Bounds for GL(3) L-Functions in the Level Aspect and Quantum Ergodicity

We establish a new subconvexity bound for the central value of L-functions associated with Hecke-Maass cusp forms on GL(3) in the level aspect. Let be a cuspidal automorphic representation of GL(3, AQ) with conductor N. We prove that L(1/2, ) N3/4 - + for some > 0, breaking the convexity barrier. Our method synthesizes the spectral reciprocity formulae of Blomer and Khan with the delta-symbol circle method developed by Munshi. As a primary application, we derive a Quantum Unique Ergodicity (QUE) result for the sequence of L2-normalized Hecke-Maass forms N of level N as N . Specifically, we show that the microlocal lifts of N equidistribute with respect to the Liouville measure on the bundle of the locally symmetric space X = SL(3, Z) SL(3, R) / SO(3). This resolves a significant case of the generalized Rudnick-Sarnak conjecture for higher-rank groups in the arithmetic aspect.