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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Equidistribution and integral points for Drinfeld modules


Authors: D. Ghioca and T. J. Tucker
Journal: Trans. Amer. Math. Soc. 360 (2008), 4863-4887
MSC (2000): Primary 11G50; Secondary 11J68, 37F10
Published electronically: April 16, 2008
MathSciNet review: 2403707
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the local height of a point on a Drinfeld module can be computed by averaging the logarithm of the distance to that point over the torsion points of the module. This gives rise to a Drinfeld module analog of a weak version of Siegel's integral points theorem over number fields and to an analog of a theorem of Schinzel's regarding the order of a point modulo certain primes.


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Additional Information

D. Ghioca
Affiliation: Department of Mathematics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1
Address at time of publication: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4
Email: dghioca@math.mcmaster.ca, dragos.ghioca@uleth.ca

T. J. Tucker
Affiliation: Department of Mathematics, Hylan Building, University of Rochester, Rochester, New York 14627
Email: ttucker@math.rochester.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04508-X
PII: S 0002-9947(08)04508-X
Keywords: Drinfeld module, heights, Diophantine approximation
Received by editor(s): September 5, 2006
Published electronically: April 16, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.