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Phd/Master thesis
Ph.D thesis
Title: A constructive theory for extensions of padic fields You can download the main document here. Master thesisEnglish title: Symmetric functions and Newton polynomials Italian title: Funzioni simmetriche e polinomi di Newton In my thesis we present the classical material of the theory of symmetric functions, with applications to the study of the characters of the symmetric group. Furthermore, we study the problem of deciding when a collection of Newton polynomials (or power sums) generate the field of rational symmetric functions. In particular, we present the following origin result: in positive characteristic p the polynomials N_{a}=x^{a}+y^{a}, N_{b}=x^{b}+y^{b}, N_{c}=x^{c}+y^{c} generate the symmetric field in x,y whenever a,b,c are relatively prime integers such that a,b,c,ab,ac,bc are prime to p. We also give a counterexample showing that it is necessary to require that the differences are prime to p. Here you can download
