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Noether forms for the study of non-composite rational functions and their spectrum

Laurent Busé, Guillaume Chèze, Salah Najib
2011 Acta Arithmetica  
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert in [19] . With this approach, some new effective results are obtained. In particular, we show that the reduction modulo p of the spectrum of a given integer multivariate rational function r coincides with the spectrum of the reduction of r modulo p for p a prime integer greater or equal to an explicit bound. This bound is
more » ... ound. This bound is given in terms of the degree, the height and the number of variables of r. With the same strategy, we also study the decomposability of r modulo p. Some similar explicit results are also provided for the case of polynomials with coefficients in A = K[Z].
doi:10.4064/aa147-3-2 fatcat:7i6voyj5qratdi73ryyqjgv5xm