Analytic expressions pertaining to certain arithmetical functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915035711799296 |
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| author | Maw, Aung Phone |
| author_facet | Maw, Aung Phone |
| contents | We demonstrate the general outlines of a method for obtaining analytic expressions for certain types of general arithmetical sums. In particular, analytical expressions for a general arithmetical sum whose terms are summed over either the positive integer solutions $(a,b)$ of the Diophantine equation $kb^2+da^2 = N$ or the positive integer solutions $(a,b)$ of the Diophantine equation $kb^2-da^2 = N$ are derived. As one of the consequences, we propose a possible improvement of the Robin-Lagarias criteria for the Riemann hypothesis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_17327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic expressions pertaining to certain arithmetical functions Maw, Aung Phone Combinatorics Number Theory 11A25, 11D09, 11M26 We demonstrate the general outlines of a method for obtaining analytic expressions for certain types of general arithmetical sums. In particular, analytical expressions for a general arithmetical sum whose terms are summed over either the positive integer solutions $(a,b)$ of the Diophantine equation $kb^2+da^2 = N$ or the positive integer solutions $(a,b)$ of the Diophantine equation $kb^2-da^2 = N$ are derived. As one of the consequences, we propose a possible improvement of the Robin-Lagarias criteria for the Riemann hypothesis. |
| title | Analytic expressions pertaining to certain arithmetical functions |
| topic | Combinatorics Number Theory 11A25, 11D09, 11M26 |
| url | https://arxiv.org/abs/2411.17327 |