A Voronoi-Oppenheim summation formula for totally real number fields (Q1729745)

The authors obtain a Voronoi-Oppenheim summation formula for divisor functions of totally real number fields. This generalizes a formula proved by \textit{A. Oppenheim} [Proc. Lond. Math. Soc. (2) 26, 295--350 (1927; JFM 53.0150.02)]. The method is similar to the one developed by \textit{J. Beineke} and \textit{D. Bump} [J. Number Theory 105, No. 1, 150--174 (2004; Zbl 1079.11041)] in order to prove the classical Oppenheim summation using a certain Eisenstein series and representation theory. The new formula has a simple formulation for real quadratic number fields.