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Shtukas and Jacobi sums. (English) Zbl 0770.11032

The analogues of Jacobi sums, in the context of function fields, introduced by the author are related to the shtukas introduced by Drinfeld. This is applied to obtain some results on the prime factorization of analogues of Gauss sums and to prove an analogue of the Gross-Koblitz formula for general function fields, generalizing the earlier results of the author. For this purpose, a new analogue of gamma function is introduced and interpolated.

MSC:

11G09 Drinfel’d modules; higher-dimensional motives, etc.
11T24 Other character sums and Gauss sums
11R58 Arithmetic theory of algebraic function fields
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References:

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