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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.09276 |
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| _version_ | 1866909989957795840 |
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| author | Gao, Liwen Guo, Xuejun |
| author_facet | Gao, Liwen Guo, Xuejun |
| contents | In this paper we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating $ζ(s)-ψ(1-s)$ as a unified analytic object, we establish its strict convexity and monotonicity on suitable intervals. Moreover, we obtain explicit boundary limits of the derivative, expressed in terms of $π$, $\log (2π)$ and Stieltjes constants. These results lead to new inequalities for $ζ(s)-ψ(1-s)$ and shed further light on the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09276 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities for $ζ(s)-ψ(1-s)$ related to a conjecture of Henry Gao, Liwen Guo, Xuejun Number Theory In this paper we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating $ζ(s)-ψ(1-s)$ as a unified analytic object, we establish its strict convexity and monotonicity on suitable intervals. Moreover, we obtain explicit boundary limits of the derivative, expressed in terms of $π$, $\log (2π)$ and Stieltjes constants. These results lead to new inequalities for $ζ(s)-ψ(1-s)$ and shed further light on the conjecture. |
| title | Inequalities for $ζ(s)-ψ(1-s)$ related to a conjecture of Henry |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.09276 |