Algebra & Number Theory

Higher-order Maass forms

Roelof Bruggeman and Nikolaos Diamantis

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729890

Digital Object Identifier
doi:10.2140/ant.2012.6.1409

Mathematical Reviews number (MathSciNet)
MR3007154

Zentralblatt MATH identifier
1286.11055

Subjects
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]

Keywords
higher-order automorphic forms Maass forms

Citation

Bruggeman, Roelof; Diamantis, Nikolaos. Higher-order Maass forms. Algebra Number Theory 6 (2012), no. 7, 1409--1458. doi:10.2140/ant.2012.6.1409. https://projecteuclid.org/euclid.ant/1513729890


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