Holomorphic quantum modular forms

Zagier, Don (2020) Holomorphic quantum modular forms. [Video]

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Quantum modular forms, which occur in connection with many number-theoretical prob-lems but also with quantum invariants of knots, are functions on the rational numbers having asomewhat non-standard weak modularity property. There are also holomorphic functions that havean analogous property and that also occur in connection with quantum invariants of knots as well asin several places in number theory. The talk will try to explain the concept and give several applica-tions and examples, including odd weight Eisenstein series for SL(2,Z) and a simpler interpretation ofthe cohomology classes (”periods”) associated to Maass cusp forms in earlier joint work with RoelofBruggeman and John Lewis.

The lecture was held within the framework of the Hausdorff Trimester Program "Dynamics: Topology and Numbers": Conference on “Transfer operators in number theory and quantum chaos”

Item Type: Video
Subjects: 1 Discrete mathematics / algebra > 11-XX Number theory
Divisions: Research > Talks
Depositing User: Axel Roenn
Date Deposited: 29 Mar 2021 16:27
Last Modified: 29 Mar 2021 16:27
URI: https://archive.mpim-bonn.mpg.de/id/eprint/4514

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