Shtukas and Jacobi sums

Summary We show how the analogues of Jacobi sums, in the context of function fields, introduced and studied in T1, T2, T3] can be obtained from shtukas introduced and studied in D2, D3, M]. We apply this 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 field, generalizing the results in T2]. For this purpose, we also introduce and interpolate a new analogue of gamma function.Oblatum 24-IV-1992 & 30-VII-1992Dedicated to the memory of Kumar Gandharva