On 3-adic valuations of generalized harmonic numbers (Q2882927)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On 3-adic valuations of generalized harmonic numbers |
scientific article; zbMATH DE number 6033000
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On 3-adic valuations of generalized harmonic numbers |
scientific article; zbMATH DE number 6033000 |
Statements
11 May 2012
0 references
generalized harmonic numbers
0 references
3-adic valuation
0 references
alternating sum
0 references
On 3-adic valuations of generalized harmonic numbers (English)
0 references
For positive integers \(m\) and \(n\), defineNEWLINENEWLINE\[NEWLINEH^{(m)}_n=\sum_{k=1}^n\frac1{k^m}\;\text{and}\;A^{(m)}_n=\sum_{k=1}^n\frac{(-1)^{k-1}}{k^m}.NEWLINE\]NEWLINENEWLINEIn the paper under review, the author determines the \(3\)-adic valuation of \(H^{(m)}_n\) and \(A^{(m)}_n\) via the \(3\)-adic expansion of \(n\).
0 references
