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arXiv · 2611.02748

When GL(2) cusp forms meet CM points in GSp(4)

Shenghao Hua·Shaoyun Yi
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Abstract

Duke's equidistribution theorem shows that the nonconstant contribution of the $\mathrm{GL}(2)$ automorphic spectrum to CM packets becomes asymptotically negligible. CM packets on the Levi base index the fibers of Bessel quotients in $\mathrm{GSp}(4)$, and the symmetric cube correspondence carries $\mathrm{GL}(2)$ cusp forms to $\mathrm{GL}(4)$. In the holomorphic setting considered here, these two constructions meet inside $\mathrm{GSp}(4)$. We prove averaged decay for the resulting class group periods over imaginary quadratic fields, expressed as averages of conditional fiber integrals. More precisely, let $f$ be a non-CM holomorphic Hecke newform with trivial central character. The mean absolute value of the associated class-group averages tends to zero along the transverse unipotent direction.

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Shenghao Hua, Shaoyun Yi. 2026-11-02. When GL(2) cusp forms meet CM points in GSp(4). https://arxiv.org/abs/2611.02748

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