Literature cited
A. O. Gel'fond, Transcendental and Algebraic Numbers [in Russian], Gostekhizdat, Moscow (1952).
K. Mahler, “Zur Approximation der Exponentialfunktion und des Logarithmus. II,” J. Reine Angew. Math.,166, 137–150 (1931).
E. Reyssat, “Un critére d'indeépendance algébrique,” J. Reine Angew. Math.,329, 66–81 (1981).
O. Zariski and P. Samuel, Commutative Algebra [Russian translation], IL, Moscow (1963).
Yu. V. Nesterenko, “Estimates of orders of zeros of functions of one class and their application to the theory of transcendental numbers,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 2, 253–284 (1977).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 35, No. 5, pp. 653–662, May, 1984.
Rights and permissions
About this article
Cite this article
Nesterenko, Y.V. Diophantine approximations in the field of p-adic numbers. Mathematical Notes of the Academy of Sciences of the USSR 35, 342–347 (1984). https://doi.org/10.1007/BF01137689
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01137689