On Ramanujan smooth expansions for a general arithmetic function
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914891225366528 |
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| author | Coppola, Giovanni |
| author_facet | Coppola, Giovanni |
| contents | We study in detail the Ramanujan smooth expansions, for arithmetic functions; we start with the most general ones, for which we supply the "$P-$local expansions", for arguments with all prime-factors $p\le P$ (namely, $P-$smooth arguments), that are also square-free; then, we supply general results for interesting subsets of arithmetic functions, regarding both their $P-$local and (global) Ramanujan smooth expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Ramanujan smooth expansions for a general arithmetic function Coppola, Giovanni Number Theory 11N37 We study in detail the Ramanujan smooth expansions, for arithmetic functions; we start with the most general ones, for which we supply the "$P-$local expansions", for arguments with all prime-factors $p\le P$ (namely, $P-$smooth arguments), that are also square-free; then, we supply general results for interesting subsets of arithmetic functions, regarding both their $P-$local and (global) Ramanujan smooth expansions. |
| title | On Ramanujan smooth expansions for a general arithmetic function |
| topic | Number Theory 11N37 |
| url | https://arxiv.org/abs/2407.19759 |