RT Journal Article
T1 Variations on inversion theorems for Newton–Puiseux series
A1 Barroso, E. R.
A1 González Pérez, Pedro Daniel
A1 Popescu-Pampu, P
AB 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 Newton-Puiseux 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.
PB Springer
SN 0025-5831
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/18096
UL https://hdl.handle.net/20.500.14352/18096
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
NO French grants
NO Labex CEMPI
DS Docta Complutense
RD 6 may 2024