A combinatorial refinement of the Kronecker-Hurwitz class number relation

math.NT

/ Authors

/ Abstract

We give a refinement of the Kronecker-Hurwitz class number relation, based on a tesselation of the Euclidean plane into semi-infinite triangles labeled by $PSL_2(\mathbb{Z})$ that may be of independent interest.

A combinatorial refinement of the Kronecker-Hurwitz class number relation

math.NT

/ Authors

Alexandru A. Popa, Don Zagier

/ Abstract

We give a refinement of the Kronecker-Hurwitz class number relation, based on a tesselation of the Euclidean plane into semi-infinite triangles labeled by $PSL_2(\mathbb{Z})$ that may be of independent interest.