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A localglobal theorem on periodic maps  ZhiWei Sun
;  Date: 
6 Apr 2004  Subject:  Number Theory; Combinatorics MSCclass: 05E99; 11A25; 11B25; 11B75; 20D60; 20F99  math.NT math.CO  Abstract:  Let $psi_1,...,psi_k$ be maps from Z to an additive abelian group with positive periods $n_1,...,n_k$ respectively. We show that the function $psi=psi_1+...+psi_k$ is constant if $psi(x)$ equals a constant for S consecutive integers x where S={r/n_s: r=0,...,n_s1; s=1,...,k}; moreover, there are periodic maps $f_0,...,f_{S1}$ from Z to Z only depending on S such that $psi(x)=sum_{r=0}^{S1}f_r(x)psi(r)$ for all integers x. This localglobal theorem extends a previous result [Math. Res. Lett. 11(2004), 187196], and has various applications.  Source:  arXiv, math.NT/0404137  Services:  Forum  Review  PDF  Favorites 


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