Higher-order Maass forms

Bruggeman, Roelof; Diamantis, Nikolaos

doi:10.2140/ant.2012.6.1409

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Higher-order Maass forms

Roelof Bruggeman and Nikolaos Diamantis

Vol. 6 (2012), No. 7, 1409–1458

DOI: 10.2140/ant.2012.6.1409

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

Vol. 6, No. 7, 2012