Grossencharakter L-functions of real quadratic fields twisted by modular symbols

摘要

Let K = Q[D~(1/2)] be a real quadratic extension of discriminant D > 0. Hecke (in 1918) [He] was the first to introduce the notion of a Grossencharakter on ideals of K. Actually, Hecke defined Grossencharakters for an arbitrary algebraic number field, but we shall not need this here. A Grossencharakter ψ is defined on principal fractional ideal (β) of K by ψ((β)) = |β/β'|~((πik)/(log∈)).