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arXiv · 1611.07146

Discrepancy of general symplectic lattices

Jayadev S. Athreya·Ioannis Konstantoulas
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Abstract

We consider random lattices taken from the general symplectic ensemble and count the number of lattice points of a typical lattice in nested families $B_t$ of certain Borel sets. Our main result is that for almost every general symplectic lattice, the discrepancy $D(Λ,B_t)$ of the lattice point count with respect to the volumes is $O(vol(B_t)^{-δ})$. This extends work of W. Schmidt who gave similar discrepancy bounds for the space of all lattices in $\mathbb{R}^n$.

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Jayadev S. Athreya, Ioannis Konstantoulas. 2018-05-13. Discrepancy of general symplectic lattices. https://arxiv.org/abs/1611.07146

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