Extensions of algebraic function fields with complete splitting of all rational places

Details Extensions of algebraic function fields with complete splitting of all rational places Extensions of algebraic function fields with complete splitting of all rational places

2000-10-19

arxiv.org/abs/math/0010194v1

Mathematics

Number Theory

18 pages

Scientific paper

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions are studied. It is then shown that quasi-symmetric polynomials are very useful in splitting rational places in extensions of function fields over finite fields and thus may be used in constructing extensions with many rational places.

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