Sieving for mass equidistribution

TL;DR

This paper investigates the holomorphic analogue of the Quantum Unique Ergodicity conjecture using the Large Sieve, focusing on shifted convolution sums and leveraging the Ramanujan-Petersson conjecture for simplifications.

Contribution

It introduces a novel approach to the holomorphic QUE conjecture by applying the Large Sieve and analyzing shifted convolution sums with new simplifications.

Findings

Successful application of the Large Sieve to the holomorphic QUE analogue

Simplified analysis due to Ramanujan-Petersson conjecture knowledge

Insights into mass equidistribution for holomorphic forms

Abstract

We approach the holomorphic analogue to the Quantum Unique Ergodicity conjecture through an application of the Large Sieve. We deal with shifted convolution sums as in ([Ho], arXiv:0809.1669), with various simplifications in our analysis due to the knowledge of the Ramanujan-Petersson conjecture in this holomorphic case.