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math.NT2022
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…
math.NT2022
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…
math.NT2022
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…