Green currents for modular cycles in arithmetic quotients of complex hyperballs

Masao Tsuzuki

Vol. 227 (2006), No. 2, 311–359

DOI: 10.2140/pjm.2006.227.311

Abstract

We obtain a Green current in the sense of Gillet–Soulé on an arithmetic quotient of a complex hyperball for the modular cycle stemming from a complex subhyperball of codimension greater than one, generalizing the classical construction of the automorphic Green function for the modular curves.

Keywords

Green current, spherical functions, Poincaré series

Mathematical Subject Classification 2000

Primary: 14G40, 11F72

Milestones

Received: 15 December 2004

Revised: 16 October 2005

Published: 1 October 2006