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On harmonic weak Maass forms associated to even integer weight newforms
Multi angle
Authors : Alfes-Neumann, Claudia (Author of the conference)
CIRM (Publisher )
11F03 - Modular and automorphic functions
11F37 - Forms of half-integer weight; nonholomorphic modular forms
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
CIRM (Publisher )
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Abstract :
In this talk we review results on several types of harmonic weak Maass forms that are related to integral even weight newforms. We start with a brief introduction to the theory of harmonic weak Maass forms. These can be related to classical modular forms via a certain differential operator, the so-called $\chi $-operator. Starting with an integral weight newform, we will review different constructions of integral weight harmonic weak Maass forms via (generalized) Weierstrass zeta functions that map to the newform under the $\chi $-operator. A second construction via theta liftings gives a half-integral weight harmonic weak Maass form whose coefficients are given by periods of certain meromorphic modular forms with algebraic coefficients and periods of the integer even weight newform. This is joint work with Jens Funke, Michael Mertens, and Eugenia Rosu resp. Jan Bruinier and Markus Schwagenscheidt.
Keywords : modular forms; harmonic weak Maass forms; periods of modular forms
MSC Codes : Keywords : modular forms; harmonic weak Maass forms; periods of modular forms
11F03 - Modular and automorphic functions
11F37 - Forms of half-integer weight; nonholomorphic modular forms
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 17/11/2023 Conference Date : 09/10/2023 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:51:06 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-09_Alfes_Neuman.mp4 
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Information on the Event
Event Title : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiquesEvent Organizers : Botero, Ana ; Freixas Montplet, Gérard ; Navarro Garmendia, Alberto ; Sombra, Martin Dates : 09/10/2023 - 13/10/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2857.html
Citation Data
DOI : 10.24350/CIRM.V.20101903Cite this video as: Alfes-Neumann, Claudia (2023). On harmonic weak Maass forms associated to even integer weight newforms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20101903 URI : http://dx.doi.org/10.24350/CIRM.V.20101903 |
See Also
- [Multi angle] Eisenstein K3 surfaces, equivariant analytic torsion, and automorphic forms on complex balls / Author of the conference Yoshikawa, Ken-Ichi.
- [Multi angle] Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$ / Author of the conference Poineau, Jérôme.
- [Multi angle] José Burgos' variations of arithmetic intersection theory / Author of the conference Kramer, Jürg.
- [Multi angle] Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated / Author of the conference Botero, Ana.
Bibliography
- ALFES-NEUMANN, Claudia et MERTENS, Michael. On Kleinian mock modular forms. arXiv preprint arXiv:2306.14466, 2023. - https://arxiv.org/abs/2306.14466
- ALFES-NEUMANN, Claudia, FUNKE, Jens, MERTENS, Michael, et al. On Jacobi--Weierstrass mock modular forms. arXiv preprint arXiv:2303.01445, 2023. - https://arxiv.org/abs/2303.01445
- ALFES-NEUMANN, Claudia, BRUINIER, Jan Hendrik, et SCHWAGENSCHEIDT, Markus. Harmonic weak Maass forms and periods II. arXiv preprint arXiv:2209.11454, 2022. - https://arxiv.org/abs/2209.11454
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