Shimizu L-function

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Shimizu L-function, introduced by <a href="/facts/Hideo_Shimizu/coCVHKGk">Hideo Shimizu</a> (1963), is a <a href="/facts/Dirichlet_series/uIAUaLcd">Dirichlet series</a> associated to a <a href="/facts/Totally_real_number_field/4rulk9kd">totally real</a> <a href="/facts/Algebraic_number_field/e0K0TXSh">algebraic number field</a>.
<a href="/facts/Michael_Atiyah/RQVJ9ATE">Michael Francis Atiyah</a>, H. Donnelly, and <a href="/facts/Isadore_Singer/YwnG6QDd">I. M. Singer</a> (1983)
defined the <a href="/facts/Signature_defect/FB8V6QH5">signature defect</a> of the boundary of a <a href="/facts/Manifold/rXPERJtu">manifold</a> as the <a href="/facts/Eta_invariant/GH8vztLa">eta invariant</a>, the value as s=0 of their eta function, and used this to show that Hirzebruch's signature defect of a cusp of a <a href="/facts/Hilbert_modular_surface/TmoIXYs8">Hilbert modular surface</a> can be expressed in terms of the value at s=0 or 1 of a Shimizu L-function.

Shimizu L-function open-in-new

Shimizu L-function