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On the Values of Partial Zeta Functions of Real Quadratic Fields at Nonpositive Integers
Author(s) -
Kallies J.,
Snyder C.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951750109
Subject(s) - mathematics , integer (computer science) , quadratic equation , arithmetic zeta function , prime zeta function , modulus , class (philosophy) , partial fraction decomposition , pure mathematics , riemann zeta function , rational function , geometry , artificial intelligence , computer science , programming language
Abstract 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 .