When GL(2) cusp forms meet CM points in GSp(4)
Abstract
Duke's equidistribution theorem shows that the nonconstant contribution of the GL(2) automorphic spectrum to CM packets becomes asymptotically negligible. CM packets on the Levi base index the fibers of Bessel quotients in GSp(4), and the symmetric cube correspondence carries GL(2) cusp forms to GL(4). In the holomorphic setting considered here, these two constructions meet inside 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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BibTeX
@misc{hua2026when,
title = {{When GL(2) cusp forms meet CM points in GSp(4)}},
author = {Shenghao Hua and Shaoyun Yi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02748},
eprint = {2611.02748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02748},
}
RIS
TY - UNPB
TI - When GL(2) cusp forms meet CM points in GSp(4)
AU - Shenghao Hua
AU - Shaoyun Yi
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02748
UR - https://arxiv.org/abs/2611.02748
AB - Duke's equidistribution theorem shows that the nonconstant contribution of the GL(2) automorphic spectrum to CM packets becomes asymptotically negligible. CM packets on the Levi base index the fibers of Bessel quotients in GSp(4), and the symmetric cube correspondence carries GL(2) cusp forms to GL(4). In the holomorphic setting considered here, these two constructions meet inside 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.
ER -