On the theory of normalized Shintani L-functions and its application to Hecke L-functions, I: Real quadratic fields

Abstract

Abstract We define the class of normalized Shintani L-functions of several variables. Unlike Shintani zeta functions, the normalized Shintani L-function is a holomorphic function. Moreover it satisfies a good functional equation. We show that Hecke L-function of a real quadratic field can be expressed as a diagonal part of some normalized Shintani L-function of several variables. This gives a good several variables generalization of a Hecke L-function of a real quadratic field.