Geodesic
The Algebraic Independence of Certain Exponential Functions
Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 968-976

Voir la notice de l'article provenant de la source Cambridge University Press

In 1897 E. Borel proved a general theorem which implied as a special case the following result equivalent to his celebrated generalization of Picard's theorem [2]: If f1 ... ,fm are entire functions such that for each, C then the functions exp f1, ... , exp f/m are linearly independent over C. In 1929 R. Nevanlinna [6] extended Borel's theorem to consider arbitrary C-linearly independent meromorphic functions < φi, ... , < φm satisfying < φ1 + ... + φm = 1. 
Brownawell, W. Dale. The Algebraic Independence of Certain Exponential Functions. Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 968-976. doi: 10.4153/CJM-1976-094-9
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[1] 1. Bochner, S. and Martin, W. T., Several complex variables (Princeton University Press, Princeton, 1948). Google Scholar

[2] 2. Borel, E., Sur les zéros des fondions entières, Acta Math. 20 (1897), 357–396. Google Scholar

[3] 3. Bundschuh, P., Kin funktiontheoretisches Analogon zum Satz von Lindemann, Archiv. d. Mathematik 25 (1974), 45–51. Google Scholar

[4] 4. Hayman, W. K., Meromorphic functions (Oxford University Press, Oxford, 1964). Google Scholar

[5] 5. Narasimhan, R., Un analogue holomorphe du théorème de Lindemann, Ann. Inst. Fourier (Grenoble) 21 (1971), 271–278. Google Scholar

[6] 6. Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes (Gauthier- Villars, Paris, 1929). Google Scholar

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