An Exceptional Arithmetic Group and its Eisenstein Series

Walter L. Baily
1970 Annals of Mathematics  
Introduction. Let GR be the simply-connected, real, Lie group of type Ei which is isogenous to the full group of holomorphic automorphisms of a bounded symmetric domain in C 27 . It is the purpose of this note to announce results on a certain arithmetic subgroup V of GR and its automorphic forms; in particular, we have proved that the automorphic forms for T given by Eisenstein series have Fourier coefficients which are rational numbers with a certain Euler product expansion. Because the proofs
more » ... Because the proofs are too long to give here, they will be presented elsewhere. In this note, all our fields are of characteristic zero; we use C, R t 0, and Z to denote respectively the complex numbers, the real numbers, the rational numbers, and the rational integers. If Fis an algebraic group, algebra, or vector space defined over Q, and if k is a field containing Q y denote by Vk the group of ^-rational points of V. It is not necessary that the family of all the fields we consider, ordered by inclusion, have a maximal element.
doi:10.2307/1970636 fatcat:75blzvvnabbrxc3s5ccx47zgn4