On lower bounds for linear forms in the values of a class of p-adic G- functions. (English) Zbl 0615.10039
L’A. considère des G-fonctions à coefficients dans un corps de nombres K plongé dans \({\mathbb{C}}_ p\). Il donne des minorations de formes linéaires à coefficients dans K en les valeurs de ces fonctions en des points de K. La borne obtenue ne dépend pas seulement d’une borne de la hauteur des coefficients, mais sépare les contributions des différents coefficients. Ce travail généralise des résultats de K. Väänänen [Acta Arith. 36, 273-295 (1980; Zbl 0369.10021)] où le corps K était très particulier.
Reviewer: F.Gramain
Keywords:
effective lowwer bounds; values at algebraic points; p-adic G-functions; linear forms; Baker’s methodReferences:
| [1] | Baker, A., Transcendental Number Theory, Cambridge University Press, Cambridge, 1975. · Zbl 0297.10013 |
| [2] | Flicker, Y. Z., Onp-adicG-functions,J. London Math. Soc., Ser. 2,15 (1977), 395–402. · Zbl 0358.10015 · doi:10.1112/jlms/s2-15.3.395 |
| [3] | Галочкин А. Ы., Оденки снизу линейныформ от значений неачений некоторыхG-функдий,Мамем. Замемку,13 (1975), 541–552. · Zbl 0324.20051 |
| [4] | Mahler K., On a paper by A. Baker on the approximation of rational powers ofe, Acta Arith.,27 (1975), 61–87. · Zbl 0305.10030 |
| [5] | Шидловский, А. Д., О критерии алгебраической независимости значений одного класса деых функдий,Изв. АН СССР, Серия Мамем.,22 (1959), 35–36. · Zbl 0342.02023 |
| [6] | Shidlovskii, A. B., On the estimates of the algebraic independence measures of the values ofE-functions,J. Austral. Math. Soc., Ser. A,27 (1979), 385–407. · doi:10.1017/S1446788700013409 |
| [7] | Siegel, C. L., Über einige Anwendungen diophantischer Approximationen,Abhandl. Preuss, Akad. Wiss. Phys.-Math. Kl., (1929), 1–70. · JFM 56.0180.05 |
| [8] | Vaaler, J. D. and van der Poorten, A. J., Bounds for solutions of systems of linear equations,Bull. Austral. Math. Soc.,25 (1982), 125–132. · Zbl 0466.10022 · doi:10.1017/S0004972700005104 |
| [9] | Väänänen, K., On linear forms of a certain class ofG-functions andp-adicG-functions,Acta Arith.,36 (1980), 273–295. |
| [10] | Waldschmidt, M., Nombres Transcendants, Lecture Notes in Mathematics, 402, Springer-Verlag, Berlin, Heidelberg, New York, 1974. |
| [11] | Xu Guangshan and Wang Lianxiang, On explicit estimates for linear forms in the values of a class ofE-functions,Bull. Austral. Math. Soc.,25 (1982), 37–69. · Zbl 0476.10030 · doi:10.1017/S0004972700005037 |
| [12] | Xu Guangshan, On linear forms in a class ofE-functions andG-functions,J. Austral. Math. Soc., Ser. A,35 (1983), 338–348. · Zbl 0534.10027 · doi:10.1017/S1446788700027038 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
