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

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

2009-06-16

arxiv.org/abs/0906.2925v1

Mathematics

Number Theory

Scientific paper

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. 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 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 polynomial ring.

Affiliated with

Also associated with

No associations

Rating

Noether's forms for the study of non-composite rational functions and their spectrum does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Noether's forms for the study of non-composite rational functions and their spectrum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noether's forms for the study of non-composite rational functions and their spectrum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-475714