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Seminar: Algebra
Vector-valued Hirzebruch-Zagier series and class number sums
Brandon Williams, UC Berkeley
Contact: David Zureick-Brown,
Venue: Mathematics and Science Center, Room W304
For any fundamental discriminant $D > 0$, Hirzebruch and Zagier constructed a modular form of weight two whose Fourier coefficients are corrections of the Hurwitz class number sums $\sum_{r^2 \equiv 4n \, (D)} H((4n - r^2) / D)$. In this talk, we will discuss how one can reinterpret their result and remove the condition that $D$ is fundamental by working instead with vector-valued modular forms for Weil representations.