Vol. 6, No. 7, 2012

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Higher-order Maass forms

Roelof Bruggeman and Nikolaos Diamantis

Vol. 6 (2012), No. 7, 1409–1458
Abstract

The spaces of Maass forms of even weight and of arbitrary order are studied. It is shown that, if we allow exponential growth at the cusps, these spaces are as large as algebraic restrictions allow. These results also apply to higher-order holomorphic forms of even weight.

Keywords
higher-order automorphic forms, Maass forms
Mathematical Subject Classification 2010
Primary: 11F12
Secondary: 11F37, 11F99, 30F35
Milestones
Received: 29 April 2011
Revised: 20 September 2011
Accepted: 27 October 2011
Published: 4 December 2012
Authors
Roelof Bruggeman
Mathematisch Instituut
Universiteit Utrecht
Postbus 80010
3508 TA Utrecht
Netherlands
Nikolaos Diamantis
School of Mathematical Science
University of Nottingham
Nottingham
NG7 2RD
United Kingdom