Hecke theory for SO+(2,n + 2)

Journal of Number Theory, vol. 262, pp. 454–470

Abstract

We describe the foundations of a Hecke theory for the orthogonal group SO+(2,n+2). In particular we consider the Hermitian modular group of degree 2 as a special example of SO+(2,4). As an application we show that the attached Maaß space is invariant under Hecke operators. This implies that the Eisenstein series belongs to the Maaß space. If the underlying lattice is even and unimodular, our approach allows us to reprove the explicit formula of its Fourier coefficients.

Authors 3

1. Aloys Krieg corresponding Aachen Lehrstuhl A für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl A für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany

2. Hannah Römer corresponding

   University of Oxford

   Affiliation as printed

   Dep. of Economics, University of Oxford, Manor Road Building, Manor Road, OX13UQ, United Kingdom

3. Felix Schaps corresponding Aachen Lehrstuhl A für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl A für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany