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- W3103103830 abstract "Let $f(x,y)$ be a complex irreducible formal power series without constant term. One may solve the equation $f(x,y)=0$ by choosing either $x$ or $y$ as independent variable, getting two finite sets of Newton-Puiseux series. In 1967 and 1968, Abhyankar and Zariski published proofs of an emph{inversion theorem}, expressing the emph{characteristic exponents} of one set of series in terms of those of the other ones. In fact, a more general theorem, stated by Halphen in 1876 and proved by Stolz in 1879, relates also the emph{coefficients} of the characteristic terms of both sets of series. This theorem seems to have been completely forgotten. We give two new proofs of it and we generalize it to a theorem concerning equations with an arbitrary number of variables." @default.
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- W3103103830 date "2016-12-03" @default.
- W3103103830 modified "2023-10-15" @default.
- W3103103830 title "Variations on inversion theorems for Newton–Puiseux series" @default.
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- W3103103830 doi "https://doi.org/10.1007/s00208-016-1503-1" @default.
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