Large values of Dirichlet polynomials with multiplicative coefficients

Q: What type of study is this?

This is a Quantitative Study study.

Zikang Dong; Yutong Song; Weijia Wang; Hao Zhang; Shengbo Zhao

doi:10.48550/arxiv.2509.09771

September 11, 2025Open Access

Large values of Dirichlet polynomials with multiplicative coefficients

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Key Points

Improved Omega results confirm behaviors of Dirichlet polynomials with multiplicative coefficients.
The study focuses on Dirichlet polynomials within the range of $rac12+ ext{ε}$ to $rac{1}{2} ext{log T}$.
Findings demonstrate significant results when $ ext{log N}$ is around $ ext{√(log T log}_2 T)$.
Research enhances the understanding of complex variables within number theory.

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Implication

Analysis reveals improved Omega results for Dirichlet polynomials, suggesting novel understandings in the field.

Abstract

In this paper, we investigate large values of Dirichlet polynomials with multiplicative coefficients ∑n≤ Nf(n)nⁱᵗ, where 1 t≤ T for large T. We prove an improved Omega result in the region exp((log T)12+ε)≤ N≤√ T, where T is large. We also show an Omega result when log N is around √log Tlog₂T.

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Cite This Study

Dong et al. (2025) studied this question.

synapsesocial.com/papers/68dc12d38a7d58c25ebb1013 https://doi.org/10.48550/arxiv.2509.09771

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Large values of Dirichlet polynomials with multiplicative coefficients

Key Points

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Implication

Abstract

Discussion

Cite This Study

Large values of Dirichlet polynomials with multiplicative coefficients

Key Points

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Implication

Abstract

Discussion

Cite This Study

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