Computational Aspects of Maass Waveforms

University dissertation from Uppsala : Matematiska institutionen

Author: Fredrik Strömberg; Uppsala Universitet.; [2005]

Keywords: NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; Maass waveform; Congruence subgroup; Noncongruence subgroup; Multiplier system; Theta multiplier system; Eta multiplier system; real weight; Hecke operator; Involution; Dirichlet character; Spectral Theory; Computation; Matematisk analys; MATHEMATICS Algebra; geometry and mathematical analysis Mathematical analysis; MATEMATIK Algebra; geometri och analys Analys; matematik; Mathematics;

Abstract: The topic of this thesis is computation of Mass waveforms, and we consider a number of different cases: Congruence subgroups of the modular group and Dirichlet characters (chapter 1); congruence subgroups and general multiplier systems and real weight (chapter 2); and noncongruence subgroups (chapter 3). In each case we first discuss the necessary theoretical background. We then outline the algorithm and display some of the results obtained by it.

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