Abstract. The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p r , where p is an odd prime number and r ≥ 2.

No abstract

No abstract

Let G be a genus of definite ternary lattices over Fq[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 representations numbers over the classes of G and for the mass of G. Our proof of the mass formula shows an interesting and seemingly new relation with certain averages of Dirichlet L-functions.

The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p r , where p is an odd prime number and r ≥ 2.