Mean values of arithmetic functions and application to sums of powers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908761875021824 |
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| author | de la Bretèche, Régis Tenenbaum, Gérald |
| author_facet | de la Bretèche, Régis Tenenbaum, Gérald |
| contents | We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hooley $Δ$-function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as some sums of powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19320 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean values of arithmetic functions and application to sums of powers de la Bretèche, Régis Tenenbaum, Gérald Number Theory 11N25, secondary 11N37, 11N64, 11P05 We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hooley $Δ$-function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as some sums of powers. |
| title | Mean values of arithmetic functions and application to sums of powers |
| topic | Number Theory 11N25, secondary 11N37, 11N64, 11P05 |
| url | https://arxiv.org/abs/2403.19320 |