Breaking the $\frac{1}{2}$-barrier for the twisted second moment of Dirichlet $L$-functions

H. M. Bui, Kyle Pratt, Nicolas Robles +1

We study the second moment of Dirichlet $L$-functions to a large prime modulus $q$ twisted by the square of an arbitrary Dirichlet polynomial. We break the $\frac{1}{2}$-barrier in…