Eisenstein-series on real, complex, and quaternionic half-spaces

Aloys Krieg

Vol. 133 (1988), No. 2, 315–354

DOI: 10.2140/pjm.1988.133.315

Abstract

The real, complex, and quaternionic half-spaces are introduced in certain analogy with the Siegel half-space. The modified symplectic group acts on the attached half-space in the usual way. At first properties of these half-spaces considered as symmetric spaces are derived. Then a fundamental domain with respect to the modified modular group, which consists of integral modified symplectic matrices, is constructed. The behavior of convergence of the corresponding Eisenstein-series is determined carefully. The Fourier-coefficients of the Eisenstein-series are calculated explicitly, whenever the degree is sufficiently small.

Mathematical Subject Classification 2000

Primary: 11F55

Secondary: 11F06

Milestones

Received: 25 October 1986

Revised: 8 July 1987

Published: 1 June 1988