Bounds for Moments of Dirichlet L-functions of fixed modulus on the
 critical line

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This is a Quantitative Study study.

Peng Gao; Liangyi Zhao

doi:10.48550/arxiv.2505.19375

May 25, 2025Open Access

Bounds for Moments of Dirichlet L-functions of fixed modulus on the critical line

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Key Points

Sharp lower bounds for the moments of Dirichlet L-functions were established for all real k ≥ 0, ensuring effective range limits.
Upper bounds were identified for the range of k from 0 to 1, offering critical insights into the behavior of these number-theoretic functions.
The study focuses on the family of Dirichlet L-functions for a fixed prime modulus, highlighting the significance of the modulus in their analysis.
This research provides essential bounds that expand understanding of moments for Dirichlet L-functions along the critical line in number theory.

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Implication

Analysis establishes sharp lower and upper bounds for Dirichlet L-functions, indicating their behavior on the critical line.

Abstract

We study the $2k$-th moment of the family of Dirichlet L-functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real k ≥ 0 and sharp upper bounds for k in the range 0 ≤ k ≤ 1.

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Cite This Study

Gao et al. (2025) studied this question.

synapsesocial.com/papers/68da58e0c1728099cfd11918 https://doi.org/10.48550/arxiv.2505.19375

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Bounds for Moments of Dirichlet L-functions of fixed modulus on the critical line

Key Points

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Implication

Abstract

Discussion

Cite This Study

Bounds for Moments of Dirichlet L-functions of fixed modulus on the critical line

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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