We prove the rationality of the Łojasiewicz exponent for p-adic semi-algebraic functions without compactness hypothesis. In the parametric case, we show that the parameter space can be divided into a finite number of semi-algebraic sets on each of which the Łojasiewicz exponent is constant.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-1-1,
author = {Azzeddine Fekak and Ahmed Srhir},
title = {Exposants de Lojasiewicz dans le cas semi-algebrique p-adique},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {1-19},
zbl = {1038.14023},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-1-1}
}
Azzeddine Fekak; Ahmed Srhir. Exposants de Lojasiewicz dans le cas semi-algebrique p-adique. Annales Polonici Mathematici, Tome 79 (2002) pp. 1-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-1-1/