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Let D be a square-free polynomial in F_q[t], where q is odd, and let G be agenus of definite ternary lattices over F_q[t] of determinant D. In this paperwe give self-contained and relatively elementary proofs of Siegel's formulasfor the weighted sum of primitive representations numbers over the classes of Gand for the mass of G. Our proof of the mass formula shows an interestingrelation with certain averages of Dirichlet L-functions.

Siegel's mass formula and averages of Dirichlet L-functions over function fields