The density of elliptic Dedekind sums
Volume 205 / 2022
Acta Arithmetica 205 (2022), 33-40
MSC: Primary 11F20; Secondary 11A15.
DOI: 10.4064/aa210921-27-7
Published online: 19 September 2022
Abstract
Elliptic Dedekind sums were introduced by R. Sczech as generalizations of classical Dedekind sums to complex lattices. We show that for any lattice with real $j$-invariant, the values of suitably normalized elliptic Dedekind sums are dense in the real numbers. This extends an earlier result of Ito for Euclidean imaginary quadratic rings. Our proof is an adaptation of the recent work of Kohnen, which gives a new proof of the density of values of classical Dedekind sums.
