Shimizu L-function
In mathematics, the Shimizu L-function, introduced by Hideo Shimizu in 1963, is a Dirichlet series associated to a totally [real number field|totally real] algebraic number field. defined the signature defect of the boundary of a manifold as the eta invariant, the value as s=0 of their eta function, and used this to show that Hirzebruch's signature defect of a cusp of a Hilbert modular surface can be expressed in terms of the value at s=0 or 1 of a Shimizu L-function.