In this article we show that the coordinates of a period lattice generator of
the n-th tensor power of the Carlitz module are algebraically independent, if
n is prime to the characteristic. The main part of the paper, however, is
devoted to a general construction for t-motives which we call prolongation,
and which gives the necessary background for our proof of the algebraic
independence. Another ingredient is a theorem which shows hypertranscendence
for the Anderson-Thakur function ω(t), i.e. that ω(t) and all its
hyperderivatives with respect to t are algebraically independent.Comment: 21 pages; v1->v2: extended the basic notation for better readability,
corrected typos; final version to appear in Documenta Mathematic