Euler-type Recurrence Relation for Arbitrary Arithmetical Function
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915530445684736 |
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| author | christopher, A. David |
| author_facet | christopher, A. David |
| contents | An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some well-known arithmetic functions. Furthermore, we derive Euler-type recurrence relations for certain partition functions and sum-of-divisors functions using infinite product identities of Jacobi and Gauss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euler-type Recurrence Relation for Arbitrary Arithmetical Function christopher, A. David Number Theory Combinatorics An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some well-known arithmetic functions. Furthermore, we derive Euler-type recurrence relations for certain partition functions and sum-of-divisors functions using infinite product identities of Jacobi and Gauss. |
| title | Euler-type Recurrence Relation for Arbitrary Arithmetical Function |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2510.01277 |