5 papers
Upper bounds for the Euclidean minima of abelian number fields
Eva Bayer-Fluckiger, Piotr Maciak
The aim of this paper is to survey and extend results concerning bounds of the Euclidean minima of abelian number fields. In particular, we give upper bounds for the Euclidean mini…
Bounds for the Euclidean minima of function fields
Piotr Maciak, Marina Monsurrò, Leonardo Zapponi
In this paper, we define Euclidean minima for function fields and give some bound for this invariant. We furthermore show that the results are analogous to those obtained in the nu…
Upper bounds for the Euclidean minima of abelian fields of odd prime power conductor
Eva Bayer-Fluckiger, Piotr Maciak
The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime conductor. In particular, these bounds imply Minkowski's conjecture for totall…
Siegel's mass formula and averages of Dirichlet L-functions over function fields
Piotr Maciak, Jorge Morales
Let D be a square-free polynomial in F_q[t], where q is odd, and let G be a genus of definite ternary lattices over F_q[t] of determinant D. In this paper we give self-contained an…
Primes of the form x^2+n*y^2 in function fields
Piotr Maciak
Let n be a square-free polynomial over F_q, where q is an odd prime power. In this paper, we determine which irreducible polynomials p in F_q[x] can be represented in the form X^2+…