K, =: an algebraic closure of K ,. K X p=: the separable algebraic closure of K in K,. G , =: the additive group over A. *Sloan fellow, also supported by NSF grant DMS-8610730(2) **Supportedby NSF grant DMS-8610730C2 , Transcendence and special zeta values in characteristic p, preprint, 1988. Added in proof. Jing Yu has also proved the transcendence of the v-adic zeta values for n not divisible by q-1.

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We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially involved relations that these multizeta values satisfy.

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