Upper bounds for $L^q$ norms of Dirichlet polynomials with small $q$

Abstract

We improve on previous upper bounds for the $q$th norm of the partial sums of the Riemann zeta function on the half line when $0<q⩽1$. In particular, we show that the 1-norm is bounded above by $(\log N{)}^{1/4}(\log \log N{)}^{1/4}$.

18 pages