Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929649273012224 |
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| author | Bruda, Glenn |
| author_facet | Bruda, Glenn |
| contents | Defining a family of recurrences, we generalize Comtet's formula for the generating function of the enumeration of indecomposable permutations. Consequently, we generalize Panaitopol's asymptotic expansion for the prime counting function, obtaining asymptotic expansions salient to the first Hardy-Littlewood conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Bruda, Glenn Combinatorics Number Theory Primary: 41A60, Secondary: 05A15 Defining a family of recurrences, we generalize Comtet's formula for the generating function of the enumeration of indecomposable permutations. Consequently, we generalize Panaitopol's asymptotic expansion for the prime counting function, obtaining asymptotic expansions salient to the first Hardy-Littlewood conjecture. |
| title | Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals |
| topic | Combinatorics Number Theory Primary: 41A60, Secondary: 05A15 |
| url | https://arxiv.org/abs/2412.19866 |