Explicit $L^2$ bounds for the Riemann $\zeta$ function

Understand

Explicit bounds on the tails of the zeta function $\zeta$ are needed for applications, notably for integrals involving $\zeta$ on vertical lines or other paths going to infinity.

• Here we bound weighted $L^2$ norms of tails of $\zeta$.
• Two approaches are followed, each giving the better result on a different range.
• The first one is inspired by the proof of the standard mean value theorem for Dirichlet polynomials.