Some classical and p-adic L-functions over number fields

Abstract

L-functions are generalizations of the Riemann zeta function. We define and study L-functions L(s,χ) attached to Hecke characters χ over number fields Q(α). Such functions converge only when Re(s)1 but have an analytic, or sometimes meromorphic, continuation to all s in the complex plane C. Moreover, we study L-functions of a p-adic variable s and calculate their special values when s is a negative integer -k.