Finite convergence over a field of power series |
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Authors: | M H Mourgues |
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Institution: | Equipe de Logique , Paris, 753, UA |
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Abstract: | In this paper, we define an analog of power series functions over R, when R is replaced by K = k((x))τ , a field of generalized power series with coefficients in an ordered field k and exponents in an ordered abelian group τ. To this end for any power series S(Y)ε KY]] and any y ε K, we define a notion of convergence of S(y). Thus to any power series S(Y) is associated a partial function S : K→ K. We show that these partial functions have a lot of similarities with analytic functions over R. Then we prove properties of zeros of such functions which extend properties of roots of polynomials over k((x))τ. |
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