An inequality of Hardy--Littlewood type for Dirichlet polynomials

Andriy Bondarenko, Winston Heap, Kristian Seip

The $L^q$ norm of a Dirichlet polynomial $F(s)={\sum }_{n=1}^N{a}_n{n}^{-s}$ is defined as \[\| F\|_q:=(\lim_{T\to\infty}\frac{1}{T}\int_{0}^T |F(it)|^qdt)^{1/q}\] for $0<q<\infty$. I…