Let be a genus of definite ternary lattices over of square-free determinant. In this paper we give self-contained and relatively elementary proofs of Siegel's formulas for the weighted sum of primitive representation numbers over the classes of and for the mass of . Our proof of the mass formula shows an interesting and seemingly new relation with certain averages of Dirichlet -functions.
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Piotr Maciak, Jorge Morales, Siegel's mass formula and averages of Dirichlet -functions over function fields. Enseign. Math. 57 (2011), no. 3/4, pp. 393–422DOI 10.4171/LEM/57-3-6