Large values of Dirichlet polynomials with multiplicative coefficients
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912584519647232 |
|---|---|
| author | Dong, Zikang Song, Yutong Wang, Weijia Zhang, Hao Zhao, Shengbo |
| author_facet | Dong, Zikang Song, Yutong Wang, Weijia Zhang, Hao Zhao, Shengbo |
| contents | 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 $\sqrt{\log T\log_2T}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large values of Dirichlet polynomials with multiplicative coefficients Dong, Zikang Song, Yutong Wang, Weijia Zhang, Hao Zhao, Shengbo Number Theory 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 $\sqrt{\log T\log_2T}$. |
| title | Large values of Dirichlet polynomials with multiplicative coefficients |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.09771 |