An estimate of approximation constants for p-adic and real varieties
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Equivalence Class Enumeration Process Enumeration Step Newton Polygon Newton Polyhedron
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References
- [1]Arjunwadkar, H. and Moh, T.T.:On the approximations of hypersurfaces PreprintGoogle Scholar
- [2]Arnol'd, V.I.:Critical points of smooth functions and their normal forms. Russian Math. Surveys, 30:5, 1975CrossRefGoogle Scholar
- [3]Arnol'd, V.I., Varchenko, A., Goussein-Zadé, S.:Singularités des applications différentiables. (en deux parties). Editions MIR, Moscou, 1986Google Scholar
- [4]Artin, M.:Algebraic approximation of structures over complete local rings. Publications Mathématiques Institut des Hautes études Scientifiques, 36, 23–58, 1969MATHMathSciNetGoogle Scholar
- [5]Becker, J., Denef, J., Lipshitz, L., van den Dries, L.:Ultraproducts and Approximation in Local Rings I. Inventiones Mathematicae. 51, 189–203, 1979MATHCrossRefMathSciNetGoogle Scholar
- [6]Berger, M.:géométrie: convexes et polytopes, polyèdres réguliers, aires et volumes. Cedic, Fernand Nathan, 1978Google Scholar
- [7]Birch, B.J., Mc Cann, K.:A criterion for the p-adic solubility of Diophantine equations. Quart. J. Math., Oxford (2), 1–23, 1984Google Scholar
- [8]Bochnak, J., Risler, J.J.:Sur les exposants de Łojasiewicz. Comment. Math. Helv. 50, 493–507, 1975MATHCrossRefMathSciNetGoogle Scholar
- [9]Bollaerts, D.:Thesis. April 1988, K.U.-LeuvenGoogle Scholar
- [10]Bröcker, T., Jänich, K.:Einführung in die Differentialtopologie. Springer Verlag, Berlin, 1973MATHGoogle Scholar
- [11]Brownawell, D.:Bounds for the degrees in the Nullstellensatz. Annals of Mathematics, 126, 577–591 1987CrossRefMathSciNetGoogle Scholar
- [12]Denef, J.:The rationality of the Poincaré series associated to the p-adic points on a variety. Inventiones Mathematicae, 77, 1–23, 1984MATHCrossRefMathSciNetGoogle Scholar
- [13]Denef, J.:Poles of p-adic complex powers and Newton polyhedra. Groupe d'étude d'Analyse ultramétrique, 12-e année, n. 17, 1984–1985Google Scholar
- [14]Denef, J.:Handwritten notes Google Scholar
- [15]Denef, J.:Poles of p-adic complex powers and Newton polyhedra. PreprintGoogle Scholar
- [16]Denef, J. and Sargos P.:Polyèdres de Newton et distributions f 3. In preparationGoogle Scholar
- [17]Denef, J. and van den Dries, L.:P-adic and real subanalytic sets. Preprint. To appear in Annals of MathematicsGoogle Scholar
- [18]Ehlers, F.:Newton polyheder und die Monodromie von Hyperflächensingularitäten. Bonner Mathematische Schriften, Bonn, 1973Google Scholar
- [19]Greenberg, M.:Rational points in henselian discrete valuation rings. Publ. Math. Inst. Hautes Etudes Sci., n. 23, 1964Google Scholar
- [20]Hironaka, H.:Introduction to real-analytic sets and real-analytic maps. Instituto matematico L. Tonelli, Pisa, 1973Google Scholar
- [21]Hörmander, L.:On the division of distribution of polynomials. Arkiv för Mathematik, band 3, n. 53, 1958Google Scholar
- [22]Khovanskii, A.G.:Newton polyhedra (resolution of singularities). Journal of Soviet Mathematics, 27, 1984Google Scholar
- [23]Khovanskii, A.G.:Newton polyhedra and toroidal singularities. Functional Analysis and its Applications, 11, 289–295, 1977CrossRefGoogle Scholar
- [24]Kneser, M.:Konstruktive Lösung p-adischer Gleichungssystemen. Göttinger Mathematische Nachrichten, 1979Google Scholar
- [25]Kouchnirenko A.G.:Polyhèdres de Newton et nombres de Milnor. Inventiones Mathematicae, 417–429, 1981Google Scholar
- [26]Kuo T.-C.:Computation of Łojasiewicz exponents and Newton polygons. Mathematica Helvetica, 1974Google Scholar
- [27]Lichtin, B.:Estimation of Łojasiewicz exponents and Newton polygons. Inventiones Mathematicae, 417–429, 1981Google Scholar
- [28]Lichtin, B. and Meuser, D.:Poles of a complex zeta function and Newton polyhedra. Compositio Mathematica, 55, 313–332, 1985.MATHMathSciNetGoogle Scholar
- [29]Łojasiewicz, S.:Ensembles sémianalytiques. I.H.E.S. Bures-Sur-Yvette, 1965Google Scholar
- [30]Malgrange, B.:Division des Distributions. Séminaire Bourbaki, 12-e année, n. 203, 1959/60Google Scholar
- [31]Milnor, J.:Singular points of complex hypersurfaces. Princeton University Press, 1968Google Scholar
- [32]Mc Mullan, P.C. and Shephard, C.G.:Convex polytopes and the upper bound conjecture. London Mathematical Society, Lecture Note series number 3, Cambridge, 1971Google Scholar
- [33]Preparata, F.:Computational geometry. Springer Verlag, 1986Google Scholar
- [34]Sargos, P.:Thèse Docteur d'état es sciences. Université de Bordeaux, 1987Google Scholar
- [35]Schappacher, N.:Ph-D thesis. Göttingen, 1978Google Scholar
- [36]Schappacher, N.:L'inégalité de Łojasiewicz ultramétrique. C.R. Acad. Sc. Paris 296, 439–442, 1983MATHMathSciNetGoogle Scholar
- [37]Schappacher, N.:Some remarks on a theorem of M.J. Greenberg. Proceedings of the 1979 Kingston Number Theory conference. Queens's Mathematical papers, 100–114, 1980Google Scholar
- [38]Schwartz, L.:Théorie des distributions, Paris, Hermann 1966MATHGoogle Scholar
- [39]Varcenko, A.N.:Newton polyhedra and estimations of oscillatory integrals. Functional Anal. and its Appl., 10, 175–196, 1977CrossRefGoogle Scholar
- [40]Varcenko, A.N.:Zetafunction of monodromy and Newton's diagram. Inventiones Mathematicae, 37, 235–262, 1976MathSciNetGoogle Scholar
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