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An integral coefficient matrix determines an integral arrangement ofhyperplanes in R^m. After modulo q reduction, the same matrix determines anarrangement A_q of ``hyperplanes'' in Z^m. In the special case of centralarrangements, Kamiya, Takemura and Terao [J. Algebraic Combin., to appear]showed that the cardinality of the complement of A_q in Z_q^m is aquasi-polynomial in q. Moreover, they proved in the central case that theintersection lattice of A_q is periodic from some q on. The present papergeneralizes these results to the case of non-central arrangements. The paperalso studies the arrangement B_m^{[0,a]} of Athanasiadis [J. Algebraic Combin.Vol.10 (1999), 207-225] to illustrate our results.

Periodicity of Non-Central Integral Arrangements Modulo Positive Integers