A classification of polyharmonic Maaß forms via quiver representations
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pullback to~$\SL{2}(\RR)$ of \emph{poly}harmonic Maa\ss{} forms for congruence
subgroups of~$\SL{2}(\ZZ)$ with exponential growth allowed at the cusps. This
extends results of Bringmann--Kudla in the harmonic case. While in the harmonic
setting there are nine cases, our classification comprises ten; A new case
arises in weights $k > 1$. To obtain the classification we introduce quiver
representations into the topic and show that those associated with polyharmonic
Maa\ss{} forms are cyclic, indecomposable representations of the two-cyclic or
the Gelfand quiver.
A classification of these transfers to a classification of polyharmonic weak
Maa\ss{} forms. To realize all possible cases of Harish-Chandra modules we
develop a theory of weight shifts for Taylor coefficients of vector-valued
spectral families. We provide a comprehensive computer implementation of this
theory, which allows us to provide explicit examples.
Zitierstile
Alfes-Neumann C, Burban I, Raum M. A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278. 2022.
Alfes-Neumann, C., Burban, I., & Raum, M. (2022). A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278
Alfes-Neumann, C., Burban, I., and Raum, M. (2022). A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278.
Alfes-Neumann, C., Burban, I., & Raum, M., 2022. A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278.
C. Alfes-Neumann, I. Burban, and M. Raum, “A classification of polyharmonic Maaß forms via quiver representations”, arXiv:2207.02278, 2022.
Alfes-Neumann, C., Burban, I., Raum, M.: A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278. (2022).
Alfes-Neumann, Claudia, Burban, Igor, and Raum, Martin. “A classification of polyharmonic Maaß forms via quiver representations”. arXiv:2207.02278 (2022).
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pullback to~$\SL{2}(\RR)$ of \emph{poly}harmonic Maa\ss{} forms for congruence
subgroups of~$\SL{2}(\ZZ)$ with exponential growth allowed at the cusps. This
extends results of Bringmann--Kudla in the harmonic case. While in the harmonic
setting there are nine cases, our classification comprises ten; A new case
arises in weights $k > 1$. To obtain the classification we introduce quiver
representations into the topic and show that those associated with polyharmonic
Maa\ss{} forms are cyclic, indecomposable representations of the two-cyclic or
the Gelfand quiver.
A classification of these transfers to a classification of polyharmonic weak
Maa\ss{} forms. To realize all possible cases of Harish-Chandra modules we
develop a theory of weight shifts for Taylor coefficients of vector-valued
spectral families. We provide a comprehensive computer implementation of this
theory, which allows us to provide explicit examples.
Zitierstile
Alfes-Neumann C, Burban I, Raum M. A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278. 2022.
Alfes-Neumann, C., Burban, I., & Raum, M. (2022). A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278
Alfes-Neumann, C., Burban, I., and Raum, M. (2022). A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278.
Alfes-Neumann, C., Burban, I., & Raum, M., 2022. A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278.
C. Alfes-Neumann, I. Burban, and M. Raum, “A classification of polyharmonic Maaß forms via quiver representations”, arXiv:2207.02278, 2022.
Alfes-Neumann, C., Burban, I., Raum, M.: A classification of polyharmonic Maaß forms via quiver representations. arXiv:2207.02278. (2022).
Alfes-Neumann, Claudia, Burban, Igor, and Raum, Martin. “A classification of polyharmonic Maaß forms via quiver representations”. arXiv:2207.02278 (2022).
Download
RDF/XML-Format
JSON-LD-Format
Turtle-Format
N3-Format