The Twisted Second Moment of the Dedekind Zeta Function of a Quadratic Field

TL;DR

This paper calculates the second moment of the Dedekind zeta function for quadratic fields combined with a Dirichlet polynomial, extending understanding of their behavior within a specific length range.

Contribution

It introduces a method to evaluate the second moment of Dedekind zeta functions multiplied by Dirichlet polynomials of a certain length, advancing analytic number theory techniques.

Findings

Explicit formula for the second moment within the specified range

Extension of previous results to more general Dirichlet polynomials

Potential applications to moments of L-functions and related conjectures

Abstract

We compute the second moment of the Dedekind zeta function of a quadratic field times an arbitrary Dirichlet polynomial of length $T^{1/11-\epsilon}$.