2 citations · 4 across the 12 of their papers we have counts for
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An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms
Christian Porter
In this paper, we revisit the theory of perfect unary forms over real quadratic fields. Specifically, we deduce an infinite family of real quadratic fields w…
Unit Reducible Cyclotomic Fields
Christian Porter, Piero Sarti, Cong Ling +1
In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic f…
Strongly Reduced Lattice Bases
Christian Porter
In this paper, we show that for each lattice basis, there exists an equivalent basis which we describe as ``strongly reduced''. We show that bases reduced in this manner exhibit ra…
On Pisot Units and the Fundamental Domain of Galois Extensions of
Christian Porter, Alexandre Bali, Alar Leibak
In this paper, we present two main results. Let be a number field that is Galois over with degree , where is the number of real embeddings and is the…
A New Bound for the Orthogonality Defect of HKZ Reduced Lattices
Christian Porter, Edmund Dable-Heath, Cong Ling
In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension . Using this result, we determine a general upper bound for the o…
An Upper Bound on the Number of Classes of Perfect Unary Forms in Totally Real Number Fields
Christian Porter, Andrew Mendelsohn
Let be a totally real number field of degree over , with discriminant and regulator respectively. In this paper, using a similar method to van Woerde…
Unit Reducible Fields and Perfect Unary Forms
Alar Leibak, Christian Porter, Cong Ling
In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furt…
Reduction Theory of Algebraic Modules and their Successive Minima
Christian Porter, Cong Ling
Lattices defined as modules over algebraic rings or orders have garnered interest recently, particularly in the fields of cryptography and coding theory. Whilst there exist many at…