Algebra & Number Theory

Higher-order Maass forms

Roelof Bruggeman and Nikolaos Diamantis

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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.

Article information

Algebra Number Theory, Volume 6, Number 7 (2012), 1409-1458.

Received: 29 April 2011
Revised: 20 September 2011
Accepted: 27 October 2011
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 11F12: Automorphic forms, one variable
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F99: None of the above, but in this section 30F35: Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]

higher-order automorphic forms Maass forms


Bruggeman, Roelof; Diamantis, Nikolaos. Higher-order Maass forms. Algebra Number Theory 6 (2012), no. 7, 1409--1458. doi:10.2140/ant.2012.6.1409.

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