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

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.