Fourier coefficients of Eisenstein series for $O^+(2, n + 2)$

TL;DR

This paper derives the Fourier expansion of Eisenstein series for the orthogonal group O(2, n+2) using classical methods, and proves their relation to Maass space at the standard cusp under certain lattice conditions.

Contribution

It provides explicit Fourier expansions for scalar-valued Eisenstein series on O(2, n+2) and establishes their belonging to the Maass space at the standard cusp.

Findings

Fourier expansion derived using classical methods.

Eisenstein series belong to the Maass space at the standard cusp.

Results hold at all local places where the lattice is maximal.

Abstract

We derive the Fourier expansion of scalar-valued Eisenstein series for O(2, n+2) using classical methods of Siegel, Braun, Zagier, Bruinier and others. We assume that the underlying lattice splits two hyperbolic planes. Finally we prove for the Eisenstein series at the standard cusp that they belong to the Maass space for O(2, n + 2), an analogue of the "Spezialschar" for Siegel modular forms introduced by Maass, at least at all local places p, where the localization of the underlying lattice is maximal.