In mathematics, the Hurwitz class number ''H''(''N''), introduced by

Adolf Hurwitz Adolf Hurwitz (; 26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory. Early life He was born in Hildesheim, then part of the Kingdom of Hanover, to a Jewish family and died ...

, is a modification of the class number of positive definite binary quadratic forms of discriminant –''N'', where forms are weighted by 2/''g'' for ''g'' the order of their automorphism group, and where ''H''(0) = –1/12. showed that the Hurwitz class numbers are coefficients of a

mock modular form In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight . The first examples of mock theta functions were described by Srinivasa Ramanu ...

of weight 3/2.

References

*{{Citation , last1=Zagier , first1=Don , title=Nombres de classes et formes modulaires de poids 3/2 , mr=0429750 , year=1975 , journal=Comptes Rendus de l'Académie des Sciences, Série A et B , issn=0151-0509 , volume=281 , issue=21 , pages=Ai, A883–A886 Number theory