The Vandermonde Determinant of the Divisors of an Integer
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918154414850048 |
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| author | Letendre, Patrick |
| author_facet | Letendre, Patrick |
| contents | Let $1=d_{1}<d_{2}< \cdots < d_{τ(n)}=n$ denote the ordered sequence of the positive divisors of an integer $n$. We are interested in estimating the arithmetic function $$ V(n) := \prod_{1 \le i < j \le τ(n)}(d_{j}-d_{i}) \quad (n \ge 1). $$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Vandermonde Determinant of the Divisors of an Integer Letendre, Patrick Number Theory 11N37, 11N56, 11N64 Let $1=d_{1}<d_{2}< \cdots < d_{τ(n)}=n$ denote the ordered sequence of the positive divisors of an integer $n$. We are interested in estimating the arithmetic function $$ V(n) := \prod_{1 \le i < j \le τ(n)}(d_{j}-d_{i}) \quad (n \ge 1). $$ |
| title | The Vandermonde Determinant of the Divisors of an Integer |
| topic | Number Theory 11N37, 11N56, 11N64 |
| url | https://arxiv.org/abs/2510.03672 |