Large values of Dirichlet polynomials with multiplicative coefficients

Abstract

In this paper, we investigate large values of Dirichlet polynomials with multiplicative coefficients ${\sum }_{n\le N}f(n)n^{it}$, where $1\ll t\le T$ for large $T$. We prove an improved Omega result in the region $\exp ((\log T{)}^{\frac{1}{2}+\epsilon })\le N\le \sqrt{T}$, where $T$ is large. We also show an Omega result when $\log N$ is around $\sqrt{\log T{\log }_{2}T}$.

11 pages