On the Values of Partial Zeta Functions of Real Quadratic Fields at Nonpositive Integers

The authors study the partial fraction decomposition of narrow class partial zeta functions of real quadratic number fields at nonpositive integer arguments and obtain an analogue of the classical v. Staudt/Clausen Theorem. The main results follow from the study of the residues of p ‐adic zeta functions associated with ray classes of modulus ( p ) for all rational primes p .