Stable automorphic forms

초록

Originally the notion of stable automorphic forms was at first introduced in the symplectic group by E. Freitag. Those such automorphic forms were called stable modular forms by Freitag. Thereafter R. Weissauer investigated stable modular forms in the sense of Freitag intensively for the study of Eisenstein series. In this paper, we generalize the concept of stable modular forms to that of stable automorphic forms on a "semisimple Lie group", a "reductive real Lie group" and a "Jacobi group". The motivation of introducing the notion of "stable automorphic forms" is to investigate the geometric properties of finite or infinite dimensional arithmetic varieties associated with those automorphic forms. Here we introduce some new notions, e.g., the universal Satake compactification, stable Jacobi forms, stable functions and so on.