On the simultaneous approximation of $a$, $b$ and $a^b$

Bijlsma, A.

On the simultaneous approximation of

a

b

and

a^{b}

Bijlsma, A.

Compositio Mathematica, Tome 35 (1977), p. 99-111 / Harvested from Numdam

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Publié le : 1977-01-01

MR 450206 | Zbl 0355.10025

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     author = {Bijlsma, Alex},
     title = {On the simultaneous approximation of $a$, $b$ and $a^b$},
     journal = {Compositio Mathematica},
     volume = {35},
     year = {1977},
     pages = {99-111},
     mrnumber = {450206},
     zbl = {0355.10025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1977__35_1_99_0}
}

Bijlsma, A. On the simultaneous approximation of $a$, $b$ and $a^b$. Compositio Mathematica, Tome 35 (1977) pp. 99-111. http://gdmltest.u-ga.fr/item/CM_1977__35_1_99_0/

Bibliographie

[1] A. Baker: Linear forms in the logarithms of algebraic numbers (II). Mathematika 14 (1967) 102-107. | Zbl 0161.05202

[2] P. Bundschuh: Zum Franklin-Schneiderschen Satz. J. Reine Angew. Math. 260 (1973) 103-118. | MR 360481 | Zbl 0256.10020

[3] P.L. Cijsouw: Transcendence measures of exponentials and logarithms of algebraic numbers. Compositio Math. 28 (1974) 163-178. | Numdam | MR 347744 | Zbl 0284.10013

[4] P.L. Cijsouw and M. Waldschmidt: Linear forms and simultaneous approximations (to appear). | Numdam | MR 447130 | Zbl 0345.10021

[5] P. Franklin: A new class of transcendental numbers. Trans. Amer. Math. Soc. 42 (1937) 155-182. | JFM 63.0155.02 | MR 1501918 | Zbl 0017.15205

[6] G.H. Hardy and E.M. Wright: An introduction to the theory of numbers, 4th edition. Oxford University Press, 1960. | MR 67125 | Zbl 0086.25803

[7] O. Perron: Die Lehre von den Kettenbrüchen. Band I, 3. Auflage. B. G. Teubner, Stuttgart, 1954. | MR 64172 | Zbl 0056.05901

[8] G. Ricci: Sul settimo problema di Hilbert. Ann. Scuola Norm. Sup. Pisa (2) 4 (1935) 341-372. | JFM 61.1085.01 | Numdam

[9] Th. Schneider: Einführung in die transzendenten Zahlen. Springer-Verlag, Berlin, 1957. | MR 86842 | Zbl 0077.04703

[10] A.A. Šmelev: A. O. Gelfond's method in the theory of transcendental numbers (in Russian). Math. Zametki 10 (1971) 415-426. English translation: Math. Notes 10 (1971) 672-678. | MR 297714 | Zbl 0254.10028

[11] M. Waldschmidt: Nombres transcendants. Lecture Notes in Mathematics 402. Springer-Verlag, Berlin, 1974. | MR 360483 | Zbl 0302.10030