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On the reduction of rank-one Drinfel'd modules

Author: David R. Hayes
Journal: Math. Comp. 57 (1991), 339-349
MSC: Primary 11G09; Secondary 11G20, 11R58
MathSciNet review: 1079021
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Abstract: The Drinfeld modules of rank one associated to all elliptic curves over the finite fields $ {\mathbb{F}_2}$ and $ {\mathbb{F}_3}$ are computed in explicit form. These examples illustrate the theory of the j-invariant of such modules as developed by Gekeler and Dorman.

References [Enhancements On Off] (What's this?)

  • [1] E. Artin, Quadratische Körper im Gebiete der höheren Kongruenzen. I, II, Math. Z. 19 (1924), 153-246. MR 1544651
  • [2] D. R. Dorman, On singular moduli for rank 2 Drinfeld modules, preprint. MR 1134255 (92h:11050)
  • [3] P. Deligne, Courbes elliptiques: formulaire, Modular Functions of One Variable, Lecture Notes in Math., vol. 476, Springer-Verlag, Berlin, 1975.
  • [4] E.-U. Gekeler, Drinfeld modular curves, Lecture Notes in Math., vol. 1231, Springer-Verlag, Berlin, 1986. MR 874338 (88b:11077)
  • [5] -, Zur Arithmetik von Drinfeld-Moduln, Math. Ann. 262 (1983), 167-182. MR 690193 (84j:12010)
  • [6] D. R. Hayes, Explicit class field theory in global function fields, Studies in Algebra and Number Theory, Adv. Math. Suppl. Stud., vol. 6, Academic Press, 1979, pp. 173-217. MR 535766 (81d:12011)

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Article copyright: © Copyright 1991 American Mathematical Society

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