Lefschetz numbers and unitary groups
1991 ◽
Vol 43
(2)
◽
pp. 193-209
◽
Keyword(s):
We give a formula for the Euler-Poincare characteristic of the fixed point set of the Cartan involution on the set of integral equivalence classes of integral unimodular hermitian forms, in terms of a product of special values of Riemann zeta functions and Dirichlet L-functions. This is done via reduction by Galois cohomology to a volume computation using the Tamagawa measure on the unitary groups.