Maaß, Hans Dirichlet series and modular forms of the second degree. (Dirichletsche Reihen und Modulformen zweiten Grades.) (German) Zbl 0273.10022 Acta Arith. 24, 225-238 (1973). This paper is a contribution to the application of differential operators in the theory of modular forms. The method is treated in the author’s lectures on “Siegel’s modular forms and Dirichlet series” [Lect. Notes Math. 216. Berlin etc.: Springer Verlag (1971; Zbl 0224.10028)]. Let \(\Omega_n\) be the real symplectic group, defined via the \(2n\times 2n\) alternating matrix \(I = \begin{pmatrix} 0 & E \\ -E & 0 \end{pmatrix}\) the \(n\times n\) identity matrix, let \(\Gamma_n\subset\Omega_n\), be the modular group of Siegel, \(A_n\) the subgroup consisting of all matrices in \(\Gamma_n\) whose lower left \(n\times n\) corner is \(0\), and let \(\Delta_n\) be the group generated by \(A_n\) and \(I\). Define \(\Omega_n^*\) analogously, when \(I\) is replaced by \(I^* = \begin{pmatrix} 0 & E \\ E & 0 \end{pmatrix}\). Then \(\Omega_n^*\) operates an the space \(\mathcal H_n^*\) of all \(n\times n\) real matrices \(W\) satisfying \(T = \tfrac12 (W+W') >0\) in the same way as \(\Omega_n\) operates on the Siegel half space \(\mathcal H_n\). The author considers the Eisenstein series Reviewer: Günter Köhler (Freiburg) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 11 Documents MSC: 11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms Citations:Zbl 0224.10028; Zbl 0086.06701 PDFBibTeX XMLCite \textit{H. Maaß}, Acta Arith. 24, 225--238 (1973; Zbl 0273.10022) Full Text: DOI EuDML Link