Counting in generic lattices and higher rank actions
| Autor: | Björklund, Michael, Gorodnik, Alexander |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider the problem of counting lattice points contained in domains in $\mathbb{R}^d$ defined by products of linear forms and we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit Theorems, provided that $d \geq 9$. We also study more refined versions pertaining to "spiraling of approximations". Our techniques are dynamical in nature and exploit effective exponential mixing of all orders for actions of higher-rank abelian groups on the space of unimodular lattices. Comment: 33 pages, 0 figures, comments are welcome |
| Databáze: | arXiv |
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