  Let K be an abelian extension of a totally real number field k, K^+ its
maximal real subfield and G=Gal(K/k). We have previously used twisted
zeta-functions to define a meromorphic CG-valued function Phi_{K/k}(s) in a way
similar to the use of partial zeta-functions to define the better-known
function Theta_{K/k}(s). For each prime number p, we now show how the value
Phi_{K/k}(0) combines with a p-adic regulator of semilocal units to define a
natural Z_pG-submodule of Q_pG which we denote {frak S}_{K/k}. If p is odd and
splits in k, our main theorem states that {frak S}_{K/k} is (at least)
contained in Z_pG. Thanks to a precise relation between Phi_{K/k}(1-s) and
Theta_{K/k}(s), this theorem can be reformulated in terms of (the minus part
of) Theta_{K/k}(s) at s=1, making it an analogue of Deligne-Ribet and
Cassou-Nogues' well-known integrality result concerning Theta_{K/k}(0). We also
formulate some conjectures including a congruence involving Hilbert symbols
that links {frak S}_{K/k} with the Rubin-Stark conjecture for K^+/k.
