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arXiv · 2508.15964

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

Shenghao Hua·Xinchen Miao
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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.

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Shenghao Hua, Xinchen Miao. 2025-08-21. Decorrelation of $\mathrm{SO}(5)\times \mathrm{SO}(2)$ Bessel periods for symmetric cubes of $\mathrm{GL}(2)$. https://arxiv.org/abs/2508.15964

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