Effective Upper Bound Estimates for $|ζ'(1/2+it)|$ via Exponential Sums

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This is a Quantitative Study study.

Ting Liu; MA Jin-jin; Bill C. H. Chang; Xiangtuan Xiong

doi:10.48550/arxiv.2510.02041

October 2, 2025Open Access

Effective Upper Bound Estimates for $|ζ'(1/2+it)|$ via Exponential Sums

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Key Points

Effective upper bounds for ζ'((1/2)+it) are derived using exponential sums, demonstrating a flexible estimation method.
Different parameters lead to varying effective upper bounds, showing the method's adaptability in applications.
The formula presented for estimating ζ'((1/2)+it) highlights the efficiency of using exponential sums in theoretical mathematics.
This research underscores the potential of leveraging exponential techniques for more accurate mathematical estimations.

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Implication

This paper derives effective upper bounds for ζ'((1/2)+it) using exponential sums, suggesting flexible parameter choices.

Abstract

In this paper, we use methods of exponential sums to derive a formula for estimating effective upper bounds of $|ζ'(1/2+it)|$. Different effective upper bounds can be obtained by choosing different parameters.

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Cite This Study

Liu et al. (2025) studied this question.

synapsesocial.com/papers/68e25385d6d66a53c2474f7c https://doi.org/10.48550/arxiv.2510.02041

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Effective Upper Bound Estimates for $|ζ'(1/2+it)|$ via Exponential Sums

Key Points

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Abstract

Discussion

Cite This Study

Effective Upper Bound Estimates for $|ζ'(1/2+it)|$ via Exponential Sums

Key Points

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Implication

Abstract

Discussion

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