Log-correlation for shifted Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields

Abstract Adapting a method of Radziwiłł and Soundararajan, we prove a generalisation of Bourgade’s central limit theorem (on shifted Riemann zeta functions) for Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields. As an application, we obtain logarithmic correlation results for shifted Dirichlet 𝐿-functions and shifted Dedekind zeta functions. These are inspired by two assumptions regarding the joint value distribution of two given shifted Riemann zeta functions, considered by Harper in le séminaire Nicolas Bourbaki.