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An extension of Hejhal’s algorithm to infinite volume fundamental domains
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Karlovitz, Alexander. An extension of Hejhal’s algorithm to infinite volume fundamental domains. Retrieved from https://doi.org/doi:10.7282/t3-jpqc-e383

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TitleAn extension of Hejhal’s algorithm to infinite volume fundamental domains
NameKarlovitz, Alexander (author); Kontorovich, Alex (chair); Iwaniec, Henryk (member); Miller, Stephen D (member); Strombergsson, Andreas (member); Rutgers University; School of Graduate Studies
Date Created2022
Other Date2022-05 (degree)
SubjectMathematics, Fuchsian groups, Hausdorff measures, Maass forms, Patterson-Sullivan theory, Flare domains
Extent100 pages : illustrations
DescriptionThis work presents an algorithm for numerically computing Maass forms and their eigenvalues for Fuchsian groups of infinite covolume. By Patterson-Sullivan theory, this has the added benefit of computing Hausdorff dimensions of the limit sets of these groups. To approximate Maass forms, we consider their Fourier expansions in different coordinate systems. To handle infinite volume fundamental domains, we introduce the concept of flare domains. We also develop theory about Fourier expansions in flare domains which mimics the classical theory on expansions with respect to cusps. Finally, we present detailed examples of the algorithm applied to symmetric Schottky groups and infinite volume Hecke groups.
NotePh.D.
NoteIncludes bibliographical references
Genretheses
Persistent URLhttps://doi.org/doi:10.7282/t3-jpqc-e383
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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