Tempered perfect lattices in the binary case
Erik Bahnson, Mark L. McConnell, Kyrie McIntosh · Journal of Number Theory · 2024
A new algorithm for computing Hecke operators for SL n was introduced in [14] . The algorithm uses tempered perfect lattices , which are certain pairs of lattices together with a quadratic form. These generalize the perfect lattices of Voronoi [17] . The present paper is the first step in characterizing tempered perfect lattices. We obtain a complete classification in the plane, where the Hecke operators are for SL 2 ( Z ) and its arithmetic subgroups. The results depend on the class field theory of orders in imaginary quadratic number fields.