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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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Kelmer et al. (2026) studied this question.
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