On the Montgomery--Vaughan weighted generalization of Hilbert's inequality
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914708324352000 |
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| author | Yangjit, Wijit |
| author_facet | Yangjit, Wijit |
| contents | This paper concerns the problem of determining the optimal constant in the Montgomery--Vaughan weighted generalization of Hilbert's inequality. We consider an approach pursued by previous authors via a parametric family of inequalities. We obtain upper and lower bounds for the constants in inequalities in this family. A lower bound indicates that the method in its current form cannot achieve any value below $3.19497$, so cannot achieve the conjectured constant $π$. The problem of determining the optimal constant remains open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_14950 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Montgomery--Vaughan weighted generalization of Hilbert's inequality Yangjit, Wijit Classical Analysis and ODEs 15A42, 26D15, 26D05 This paper concerns the problem of determining the optimal constant in the Montgomery--Vaughan weighted generalization of Hilbert's inequality. We consider an approach pursued by previous authors via a parametric family of inequalities. We obtain upper and lower bounds for the constants in inequalities in this family. A lower bound indicates that the method in its current form cannot achieve any value below $3.19497$, so cannot achieve the conjectured constant $π$. The problem of determining the optimal constant remains open. |
| title | On the Montgomery--Vaughan weighted generalization of Hilbert's inequality |
| topic | Classical Analysis and ODEs 15A42, 26D15, 26D05 |
| url | https://arxiv.org/abs/2203.14950 |