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The Algebraic Independence of Certain Exponential Functions

Published online by Cambridge University Press:  20 November 2018

W. Dale Brownawell
W. Dale Brownawell*
Affiliation:
Pennsylvania State University, University Park, Pennsylvania
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 968 - 976
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bochner, S. and Martin, W. T., Several complex variables (Princeton University Press, Princeton, 1948).Google Scholar
2. Borel, E., Sur les zéros des fondions entières, Acta Math. 20 (1897), 357–396.Google Scholar
3. Bundschuh, P., Kin funktiontheoretisches Analogon zum Satz von Lindemann, Archiv. d. Mathematik 25 (1974), 45–51.Google Scholar
4. Hayman, W. K., Meromorphic functions (Oxford University Press, Oxford, 1964).Google Scholar
5. Narasimhan, R., Un analogue holomorphe du théorème de Lindemann, Ann. Inst. Fourier (Grenoble) 21 (1971), 271–278.Google Scholar
6. Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes (Gauthier- Villars, Paris, 1929).Google Scholar