An alternate approach to solitons for F-q[t]

We describe an alternate approach to the solitons for F-q[t] introduced by Anderson. The product of the monic polynomials in F-q[t] of degree i in a g iven congruence class can be expressed in a compact form by the solitons "f or all i at once." They also link the arithmetic of F-q[t] gamma values at fractions to the analogues of Jacobians of Fermat curves in the setting of higher dimensional generalizations of Drinfeld modules. We will calculate e xplicit equations, formulae and bound the support of the divisors of the so litons. We also show how the generalization of this approach differs from t he one suggested by Anderson's approach. (C) 1999 Academic Press.