Der Satz von Hurwitz beim Jacobialgorithmus

Abstract

Letx be a point such that its expansion by Jacobi's algorithm does not possess “Störungen” (in the sense ofPerron). Let

$$F(x,g) = \frac{{A_{_0 }^{(g + n + 1)} + \sum\limits_{j = 1}^n {A_0^{(g + j)} x_j^{(g)} } }}{{A_{_0 }^{(g + 1)} }}$$

and let ξ>1 satisfy ξn+1=ξn+1. Then at least one of 2n+1 consecutive values of g satisfiesF(x,g) > ξn+nξn−1.