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Shimizu L-function : ウィキペディア英語版
Shimizu L-function
In mathematics, the Shimizu L-function, introduced by , is a Dirichlet series associated to a 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.
==Definition==

Suppose that ''K'' is a totally real algebraic number field, ''M'' is a lattice in the field, and ''V'' is a subgroup of maximal rank of the group of totally positive units preserving the lattice. The Shimizu L-series is given by
:L(M,V,s) = \sum_ \frac

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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