On the orders of zero of certain functions
Fonctions abéliennes et nombres transcendants, Mémoires de la Société Mathématique de France, Serie 2 no. 2  (1980), p. 5-20
@incollection{MSMF_1980_2_2__5_0,
     author = {Brownawell, W. Dale},
     title = {On the orders of zero of certain functions},
     booktitle = {Fonctions ab\'eliennes et nombres transcendants},
     editor = {Bertrand, Daniel and Waldschmidt, Michel},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {2},
     year = {1980},
     pages = {5-20},
     zbl = {0467.10024},
     mrnumber = {82k:10038},
     language = {mul},
     url = {http://www.numdam.org/item/MSMF_1980_2_2__5_0}
}
Brownawell, W. Dale. On the orders of zero of certain functions, in Fonctions abéliennes et nombres transcendants, Mémoires de la Société Mathématique de France, Serie 2, no. 2 (1980), pp. 5-20. doi : 10.24033/msmf.274. http://www.numdam.org/item/MSMF_1980_2_2__5_0/

[1] W. D. Brownawell and D. W. Masser, Multiplicity estimates for analytic functions II. | Zbl 0461.10027

[2] W. Gröbner, Moderne Algebraische Geometrie, die idealtheoretischen Grundlagen, Springer Verlag, Wien und Innsbruck, 1949. | Zbl 0033.12706

[3] W. Krull, Idealtheorie, 2nd expanded printing, Springer Verlag, Berlin, 1968. | MR 37 #5197 | Zbl 0155.36401

[4] Ju. V. Nesterenko, Estimates for the orders of zero of some functions of a certain class and their application in the theory of transcendental numbers, Izv. Akad. Nauk SSR, Ser. Mat. 41 (1977), 253-284, Math. USSR Izv. 11 (1977), 239-279, (see also these Proceedings). | Zbl 0378.10022

[5] O. Zariski and P. Samuel, Commutative Algebra, Volumes I and II, Springer Verlag, New York, 1968. | Zbl 0322.13001