Lewis–Zagier correspondence for higher-order forms

Anton Deitmar

Vol. 249 (2011), No. 1, 11–21

DOI: 10.2140/pjm.2011.249.11

Abstract

The Lewis–Zagier correspondence attaches period functions to Maaß wave forms. We extend this correspondence to wave forms of higher order, which are higher-order invariants of the Fuchsian group in question. The key ingredient, an identification of higher-order invariants with ordinary invariants of unipotent twists, makes it possible to apply standard methods of automorphic forms to higher-order forms.

Keywords

higher-order invariants, automorphic forms

Mathematical Subject Classification 2000

Primary: 11F12, 11F67

Milestones

Received: 29 September 2009

Revised: 19 April 2010

Accepted: 27 April 2010

Published: 3 January 2011