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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linear independence and divided derivatives of a Drinfeld module II


Authors: W. Dale Brownawell and Laurent Denis
Journal: Proc. Amer. Math. Soc. 128 (2000), 1581-1593
MSC (2000): Primary 11J93, 11G09
Published electronically: February 25, 2000
MathSciNet review: 1709742
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Abstract:

In this note we extend our previous results on the linear independence of values of the divided derivatives of exponential and quasi-periodic functions related to a Drinfeld module to divided derivatives of values of identity and quasi-periodic functions evaluated at the logarithm of an algebraic value. The change in point of view enables us to deal smoothly with divided derivatives of arbitrary order. Moreover we treat a full complement of quasi-periodic functions corresponding to a basis of de Rham cohomology.


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Additional Information

W. Dale Brownawell
Affiliation: Department of Mathematics, Penn State University, University Park, Pennsylvania 16802
Email: wdb@math.psu.edu

Laurent Denis
Affiliation: U.F.R. de Mathématiques Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France
Email: ladenis@ccr.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05633-1
PII: S 0002-9939(00)05633-1
Keywords: Drinfeld modules, transcendence, linear independence, divided derivatives
Received by editor(s): May 13, 1998
Published electronically: February 25, 2000
Additional Notes: The first author was supported in part by an NSF Grant.
Dedicated: This paper is dedicated to the memory of Bernard Dwork
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society