On the number of finite non-isomorphic Abelian groups in short intervals (Q1334085)
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 the number of finite non-isomorphic Abelian groups in short intervals |
scientific article; zbMATH DE number 640468
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of finite non-isomorphic Abelian groups in short intervals |
scientific article; zbMATH DE number 640468 |
Statements
On the number of finite non-isomorphic Abelian groups in short intervals (English)
0 references
4 April 1995
0 references
The author announces, without proof, the result that \[ \sum_{x<n\leq x+h,\;a(n)=k} 1= (P_ k+ o(1))h+ O(x^{1057/ 4785+ \varepsilon}). \] Here \(a(n)\) denotes the number of non-isomorphic Abelian groups with \(n\) elements, and \(P_ k\geq 0\) is a suitable constant depending on \(k\).
0 references
short intervals
0 references
asymptotic formula
0 references
number of non-isomorphic abelian groups
0 references
1.0000001
0 references
0.9890671
0 references
0.9128721
0 references
0.9107299
0 references
0.9107299
0 references
0 references
0.8995428
0 references
