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arXiv · 2509.09771

Large values of Dirichlet polynomials with multiplicative coefficients

Zikang Dong·Yutong Song·Weijia Wang·Hao Zhang·Shengbo Zhao
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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 $\exp((\log T)^{\frac12+\varepsilon})\le N\le\sqrt T$, where $T$ is large. We also show an Omega result when $\log N$ is around $\sqrt{\log T\log_2T}$.

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Zikang Dong, Yutong Song, Weijia Wang, Hao Zhang, Shengbo Zhao. 2025-09-11. Large values of Dirichlet polynomials with multiplicative coefficients. https://arxiv.org/abs/2509.09771

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