Abstract

We introduce invariants of lattices in real quadratic fields that are constructed from the first derivative at s = 0 of certain L-series. These invariants are able to distinguish the contribution of each of the two embeddings of the base field into ?. Our construction makes use of the first cohomology group of PGL2(?) with coefficients in a module of distributions. This technique allows us to control and sometimes remove the effect of choosing coordinates in the description of such lattices. Furthermore, we explicitly compute the invariants in the simplest cases. © 2025 Independent University of Moscow.