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On harmonic weak Maass forms associated to even integer weight newforms

By Claudia Alfes-Neumann

Appears in collection : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiques

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.

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Citation data

  • DOI 10.24350/CIRM.V.20101903
  • Cite this video Alfes-Neumann Claudia (10/9/23). On harmonic weak Maass forms associated to even integer weight newforms. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20101903
  • URL https://dx.doi.org/10.24350/CIRM.V.20101903

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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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