Siegelsche Modulfunktionen

Siegel Modular Forms and Their Applications

“…Then θ B,P is a classical Siegel modular form in M k+r/2 (Γ g ), see [29]. Such theta series for P ∈ H k−r/2,g and B as above span a subspace of M k (Γ g ) that is invariant under the Hecke-operators that will be introduced later, cf.…”

“…In particular, for n ≥ 3 the Euler number of the manifold Γ g (n)\H g equals [Γ g (1) : Γ g (n)]ζ(−1) · · · ζ(1 − 2g). We first present two exercises for the solution of which we refer to [29].…”

“…Finally, we would like to make a reference to Siegel's Hauptsatz [95] (or [29], p. 285) on representations of quadratic forms by quadratic forms which can be viewed as an identity between an Eisenstein series and a weighted sum of theta series, and to its far-reaching generalizations, cf. [67].…”

“…For this and an analysis of when the other forms extend over the singularities in these cases we refer to [105,29].…”

“…A good introduction to the Siegel modular group and Siegel modular forms is Freitag's book [29]. The reader may also consult the introductory book by Klingen [60].…”