Zeta-functions of binary Hermitian forms
Motivated by the work of \textit{J. Elstrodt}, \textit{F. Grunewald} and \textit{J. Mennicke} on zeta-functions of binary Hermitian forms [Math. Ann. 277, 655--708 (1987; Zbl 0659.10021)] the author investigates zeta-functions of binary Hermitian forms over the ring of integers of the extension \(\mathbb{Q} (i, \sqrt {2})\) over \(\mathbb{Q} (\sqrt {2})\). For any integer \(\Delta\) of \(\mathbb{Q} (\sqrt {2})\) an associated zeta-function \(Z (\Delta, s)\) is defined. This zeta-function has an Euler product expansion. The main result of the work under review is an explicit determination of the coefficients of the Euler factors of \(Z (\Delta, s)\). This yields an explicit formula for the Euler product of \(Z (\Delta, s)\).
scientific article; zbMATH DE number 794481