English
On harmonic weak Maass forms associated to even integer weight newforms
Multi angle
Auteurs : Alfes-Neumann, Claudia (Auteur de la conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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.
Mots-Clés : modular forms; harmonic weak Maass forms; periods of modular forms
Codes MSC : Mots-Clés : 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 17/11/2023 Date de Captation : 09/10/2023 Sous Collection : Research talks Catégorie arXiv : Number Theory Domaine(s) : Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 00:51:06 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-10-09_Alfes_Neuman.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiquesOrganisateurs de la Rencontre : Botero, Ana ; Freixas Montplet, Gérard ; Navarro Garmendia, Alberto ; Sombra, Martin Dates : 09/10/2023 - 13/10/2023 Année de la rencontre : 2023 URL de la Rencontre : https://conferences.cirm-math.fr/2857.html
Données de citation
DOI : 10.24350/CIRM.V.20101903Citer cette vidéo: 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 |
Voir Aussi
- [Multi angle] Eisenstein K3 surfaces, equivariant analytic torsion, and automorphic forms on complex balls / Auteur de la conférence Yoshikawa, Ken-Ichi.
- [Multi angle] Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$ / Auteur de la conférence Poineau, Jérôme.
- [Multi angle] José Burgos' variations of arithmetic intersection theory / Auteur de la conférence Kramer, Jürg.
- [Multi angle] Rings of Siegel-Jacobi forms of bounded relative index are not finitely generated / Auteur de la conférence Botero, Ana.
Bibliographie
- 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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