Fall 2024
After a long hiatus, we are resuming in-person talks in our newly renovated mathematics building. The seminar typically runs on Fridays from 2:30-4:30 in LC 315. For more information, contact Alex Duncan .
| Date | Location | Speaker | Title | Host |
| Friday, Sep 13 3:30PM |
Candace Bethea Duke University |
TBA | ||
| Friday, Sep 20 3:03PM |
Michael Nelson Clemson University |
TBA | Vraciu | |
| Friday, Sep 27 3:30PM |
Andreas Mono Vanderbilt University |
A Modular Framework for Generalized Hurwitz Class Numbers |
Abstracts
Candace Bethea - TBA
TBA
Michael Nelson - TBA
Andreas Mono - A Modular Framework for Generalized Hurwitz Class Numbers
We discover a simple relation between the mock modular generating functions of the level 1 and level \(N\) Hurwitz class numbers. This relation gives rise to a holomorphic modular form of weight \(\frac{3}{2}\) and level \(4N\) for \(N > 1\) odd and square-free. We extend this observation to a non-holomorphic framework and obtain a higher level analog of Zagier’s Eisenstein series as well as a preimage under the Bruinier–Funke operator. All of these observations are deduced from a more general inspection of the weight \(\frac{1}{2}\) Maass–Eisenstein series of level \(4N\) at its spectral point \(s = \frac{3}{4}\). This idea goes back to Duke, Imamoğlu and Tóth in level 4 and relies on the theory of so-called sesquiharmonic Maass forms. This is joint work with Olivia Beckwith.