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Barroso, E. R. and González Pérez, Pedro Daniel and PopescuPampu, P (2017) Variations on inversion theorems for Newton–Puiseux series. Mathematische Annalen, 368 (34). pp. 13591397. ISSN 00255831

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Official URL: https://link.springer.com/article/10.1007/s0020801615031
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http://dx.doi.org/10.1007/s0020801615031  Publisher 
Abstract
Let f (x, y) be an irreducible formal power series without constant term, over an algebraically closed field of characteristic zero. One may solve the equation f (x, y) = 0 by choosing either x or y as independent variable, getting two finite sets of NewtonPuiseux series. In 1967 and 1968 respectively, Abhyankar and Zariski published proofs of an inversion theorem, expressing the characteristic exponents of one set of series in terms of those of the other set. In fact, a more general theorem, stated by Halphen in 1876 and proved by Stolz in 1879, relates also the 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 irreducible series with an arbitrary number of variables.
Item Type:  Article 

Uncontrolled Keywords:  Branch; Characteristic exponents; Plane curve singularities; Hypersurface singularities; Quasiordinary series; Lagrange inversion; NewtonPuiseux serie 
Subjects:  Sciences > Mathematics > Functions Sciences > Mathematics > Algebraic geometry 
ID Code:  44737 
Deposited On:  22 Sep 2017 11:21 
Last Modified:  25 Sep 2017 08:18 
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