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Effective Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces
Abstract
We prove an effective joint equidistribution theorem for d-dimensional K-subspaces, 1≤ d<n, of a fixed n-dimensional rigid adelic space over a number field K. The parameters are the height, the image in the archimedean Grassmannian, and the isometry classes of the subspace and quotient after each is rescaled to height $1$. For bounded Lipschitz test functions, the error term is power-saving with an explicit exponent. As an application, our theorem refines Thunder's asymptotic formula for subspaces of bounded height. We also obtain a power-saving asymptotic for subspaces containing d linearly independent projective points of bounded height, with a leading constant expressed as a moment of the last successive minimum.
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BibTeX
@misc{di2026effective,
title = {{Effective Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces}},
author = {Ruida Di},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.30608},
eprint = {2608.30608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30608},
}
RIS
TY - UNPB
TI - Effective Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces
AU - Ruida Di
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2608.30608
UR - https://arxiv.org/abs/2608.30608
AB - We prove an effective joint equidistribution theorem for d-dimensional K-subspaces, 1≤ d<n, of a fixed n-dimensional rigid adelic space over a number field K. The parameters are the height, the image in the archimedean Grassmannian, and the isometry classes of the subspace and quotient after each is rescaled to height $1$. For bounded Lipschitz test functions, the error term is power-saving with an explicit exponent. As an application, our theorem refines Thunder's asymptotic formula for subspaces of bounded height. We also obtain a power-saving asymptotic for subspaces containing d linearly independent projective points of bounded height, with a leading constant expressed as a moment of the last successive minimum.
ER -