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INDEX-CLASS NUMBER FORMULAS OVER GLOBAL FUNCTION FIELDS
Published online by Cambridge University Press: 04 December 2007
Abstract
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.
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- © 1997 Kluwer Academic Publishers
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