A lower bound for periods of matrices
Corvaja, Pietro ; Rudnick, Zeev ; Zannier, Umberto
arXiv, 0309215 / Harvested from arXiv
Text on arXiv
For a nonsingular integer matrix A, we study the growth of the order of A modulo N. We say that a matrix is exceptional if it is diagonalizable, and a power of the matrix has all eigenvalues equal to powers of a single rational integer, or all eigenvalues are powers of a single unit in a real quadratic field. For exceptional matrices, it is easily seen that there are arbitrarily large values of N for which the order of A modulo N is logarithmically small. In contrast, we show that if the matrix is not exceptional, then the order of A modulo N goes to infinity faster than any constant multiple of log N.
Publié le : 2003-09-12
Classification:  Mathematics - Number Theory,  Mathematical Physics,  Nonlinear Sciences - Chaotic Dynamics,  11A07,  11Jxx 
@article{0309215,
     author = {Corvaja, Pietro and Rudnick, Zeev and Zannier, Umberto},
     title = {A lower bound for periods of matrices},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309215}
}

Corvaja, Pietro; Rudnick, Zeev; Zannier, Umberto. A lower bound for periods of matrices. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309215/