Decorrelation of $\mathrm{SO}(5)\times \mathrm{SO}(2)$ Bessel periods for symmetric cubes of $\mathrm{GL}(2)$

TL;DR

This paper investigates how Bessel periods associated with symmetric cube lifts of GL(2) forms decorrelate on average over imaginary quadratic fields, under the assumption of GRH, revealing new insights into their distribution.

Contribution

It establishes a decorrelation phenomenon for global Bessel periods of symmetric cube lifts of GL(2) forms, conditional on GRH, advancing understanding of their statistical behavior.

Findings

Decorrelation of Bessel periods observed under GRH

Average behavior over imaginary quadratic fields analyzed

Conditional results contribute to automorphic form theory

Abstract

We demonstrate that for symmetric cubes of algebraic regular Hecke eigenforms on $\mathrm{GL}(2)$, a decorrelation phenomenon occurs for global Bessel periods of $\mathrm{SO}(5)\times \mathrm{SO}(2)$ averaged over imaginary quadratic fields, conditional on the Generalized Riemann Hypothesis.