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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.

Information

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