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Automata and transcendence of the Tate period in finite characteristic

Authors: Jean-Paul Allouche and Dinesh S. Thakur
Journal: Proc. Amer. Math. Soc. 127 (1999), 1309-1312
MSC (1991): Primary 11J89, 11G07, 68Q68, 11B85
Published electronically: January 27, 1999
MathSciNet review: 1476112
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Abstract: Using the techniques of automata theory, we give another proof of the function field analogue of the Mahler-Manin conjecture and prove transcendence results for the power series associated to higher divisor functions $\sigma _k(n)=\sum _{d|n}d^k$.

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Additional Information

Jean-Paul Allouche
Affiliation: CNRS, LRI, Bâtiment 490, Université d’Orsay F-91405 Orsay Cedex, France

Dinesh S. Thakur
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Keywords: Transcendence, periods, elliptic curves, automata, recognizability
Received by editor(s): August 27, 1997
Published electronically: January 27, 1999
Additional Notes: The second author was supported in part by NSF grant DMS 9623187.
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society

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