Publication: Natural density of rectangular unimodular integer matrices
Natural density of rectangular unimodular integer matrices
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Maze, G., Rosenthal, J., & Wagner, U. (2011). Natural density of rectangular unimodular integer matrices. Linear Algebra and Its Applications, 434(5), 1319–1324. https://doi.org/10.1016/j.laa.2010.11.015
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An integer matrix of size k×n, k≤n, is called unimodular if it can be extended to an n×n invertible matrix. The natural density of unimodular k×n matrices, which may be explained as the “probability" of a random k×n integer matrix to be unimodular, is determined in this paper using the Riemann's zeta function. The present result is a generalization of a classical result due to Cesáro and is also related to Quillen-Suslin's Theorem .
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- Maze, G
- Rosenthal, J
- Wagner, U
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Maze, G., Rosenthal, J., & Wagner, U. (2011). Natural density of rectangular unimodular integer matrices. Linear Algebra and Its Applications, 434(5), 1319–1324. https://doi.org/10.1016/j.laa.2010.11.015
