Erratum to: On the Geometry of Cyclic Lattices

A mistake in the results of our previous paper is corrected. Theorems 1.1 and 1.2 of our paper [1] are incorrect as stated. Specifically, these theorems assert that the well-rounded (WR) lattices comprise a positive proportion of all cyclic lattices in every dimension.This assertion is basedon comparative asymptotic counting estimates for WR cyclic lattices versus all cyclic lattices with successive minima bounded by R as R → ∞. While the lower bound on the number of WR cyclic lattices produced in Sect. 4 is correct, the upper bound on the number of all cyclic lattices produced in Sect. 3 (specifically, Lemmas 3.2 and 3.3) is not accurate. Similarly, in the case N = 2, there is a mistake in the estimate on the function h2(R) in the proof of Lemma 5.2, while the rest of Lemma 5.2 is correct. For the purposes of our current results, this means that WR cyclic lattices do not comprise a positive proportion of all cyclic lattices in a given dimension, and hence our results should instead be stated as counting estimates on the number of WR cyclic lattices. This