Geodesic
Approximation of Holomorphic Solutions of a System of Real Analytic Equations
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 752-761

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DOI

We prove the existence of an approximation function for holomorphic solutions of a system of real analytic equations. For this we use ultraproducts andWeierstrass systems introduced by J. Denef and L. Lipshitz. We also prove a version of the Płoski smoothing theorem in this case.
DOI : 10.4153/CMB-2011-129-4
Mots-clés : 13B40, 13L05, 14F12, Artin approximation, real analytic equations 
Hickel, M.; Rond, G. Approximation of Holomorphic Solutions of a System of Real Analytic Equations. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 752-761. doi: 10.4153/CMB-2011-129-4
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     author = {Hickel, M. and Rond, G.},
     title = {Approximation of {Holomorphic} {Solutions} of a {System} of {Real} {Analytic} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {752--761},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-129-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-129-4/}
}
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