Effective decorrelation of Hecke eigenforms

TL;DR

This paper proves effective quantitative decorrelation of Hecke eigenforms' values at large weights, leading to an effective understanding of their mass and zero distribution, advancing the analytic theory of automorphic forms.

Contribution

It introduces an effective method to quantify decorrelation of Hecke eigenforms, improving previous qualitative results in automorphic form theory.

Findings

Quantitative decorrelation of Hecke eigenforms established

Effective equidistribution of mass demonstrated

Zeros of linear combinations of eigenforms are shown to distribute effectively

Abstract

In this paper, we prove effective quantitative decorrelation of values of two Hecke eigenforms as the weight goes to infinity. As consequences, we get an effective version of equidistribution of mass and zeros of certain linear combinations of Hecke eigenforms.