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INDEX-CLASS NUMBER FORMULAS OVER GLOBAL FUNCTION FIELDS

Published online by Cambridge University Press:  04 December 2007

LINSHENG YIN
LINSHENG YIN
Affiliation:
Department of Mathematical Science, University of Tokyo, Tokyo 153, Japan
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Abstract

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In classical number theory, one has the famous theorem of Kummer-Sinnott giving the index of the cyclotomic units in the total unit group. Using the division values of sgn-normalized rank one Drinfeld modules, we construct the group of extended cyclotomic units for an abelian extension of a global function field and calculate its index in the whole unit group. The result could be regarded as an analogue and a generalization of Kummer-Sinnott's.

Keywords

sgn-normalized rank one Drinfeld modulesextended cyclotomic unitsindex-class number formula
Type
Research Article
Information
Compositio Mathematica , Volume 109 , Issue 1 , October 1997 , pp. 49 - 66
Copyright
© 1997 Kluwer Academic Publishers