JournalslemVol. 57, No. 3/4pp. 393–422

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

  • Piotr Maciak

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
  • Jorge Morales

    Louisiana State University, Baton Rouge, USA
Siegel's mass formula and averages of Dirichlet $L$-functions over function fields cover
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Abstract

Let G\mathfrak G be a genus of definite ternary lattices over Fq[t]\mathbb F_q[t] 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 G\mathfrak G and for the mass of G\mathfrak G. Our proof of the mass formula shows an interesting and seemingly new relation with certain averages of Dirichlet LL-functions.

Cite this article

Piotr Maciak, Jorge Morales, Siegel's mass formula and averages of Dirichlet LL-functions over function fields. Enseign. Math. 57 (2011), no. 3, pp. 393–422

DOI 10.4171/LEM/57-3-6