In
mathematics, the signature defect of a singularity measures the correction that a singularity contributes to the signature theorem.
introduced the signature defect for the cusp singularities of
Hilbert modular surface
In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular variet ...
s.
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
In mathematics, the Shimizu ''L''-function, introduced by , 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 ...
.
References
*
*{{Citation , last1=Hirzebruch , first1=Friedrich E. P. , title=Hilbert modular surfaces , doi=10.5169/seals-46292 , mr=0393045 , year=1973 , journal=L'Enseignement Mathématique , series=2e Série , issn=0013-8584 , volume=19 , pages=183–281
Singularity theory