Arithmetic Dijkgraaf-Witten invariants for real quadratic fields, quadratic residue graphs, and density formulas

Yuqi Deng, Riku Kurimaru, Toshiki Matsusaka

We compute Hirano's formula for the mod 2 arithmetic Dijkgraaf-Witten invariant $Z_k$ for the ring of integers of the quadratic field $k=\mathbb{Q}(\sqrt{p_1\cdots p_r})$, where…