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Second moment of incomplete Eisenstein series revisited
Abstract
We revisit Yu's second moment formula for incomplete Eisenstein series and give uniform bounds for secondary terms appearing in this formula. We use these bounds to improve results on distribution of integer points on the light cone corresponding to an indefinite quadratic form, as well as intrinsic Diophantine approximation on ellipsoids, and counting holonomy vectors of saddle connections of Veech surfaces.
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BibTeX
@misc{kelmer2026second,
title = {{Second moment of incomplete Eisenstein series revisited}},
author = {Dubi Kelmer and Shucheng Yu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05764},
eprint = {2611.05764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05764},
}
RIS
TY - UNPB
TI - Second moment of incomplete Eisenstein series revisited
AU - Dubi Kelmer
AU - Shucheng Yu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05764
UR - https://arxiv.org/abs/2611.05764
AB - We revisit Yu's second moment formula for incomplete Eisenstein series and give uniform bounds for secondary terms appearing in this formula. We use these bounds to improve results on distribution of integer points on the light cone corresponding to an indefinite quadratic form, as well as intrinsic Diophantine approximation on ellipsoids, and counting holonomy vectors of saddle connections of Veech surfaces.
ER -