Speaker: Prof. Haitcie Boylan (Istanbul University)

Title: Hurwitz class numbers in the theory of automorphic forms, and an extension to totally real number fields

Time: 10:00-11:30 September 8, 2026 (Tuesday)

Inviter: Prof. Ye Tian (MCM)

Place: MCM110

Abstract: Hurwitz class numbers H(N), counting equivalence classes of integral binary quadratic forms of discriminant −N, play a central role in the theory of automorphic forms—appearing as Fourier coefficients of half integral weight Eisenstein series, in the Eichler–Selberg trace formula, and in counting elements of given characteristic polynomial in quaternion orders via Jacobi forms. This talk surveys these classical connections and presents an extension of Hurwitz class numbers to totally real fields, defining H(∆,K) via special values L(χ_∆,0), and deriving ex plicit finite formulas relating them to class numbers of K and K(√∆).