The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.
The determinants of GCD matrices
โ Scribed by Zhongshan Li
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 319 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let : 1 , ..., : k be partitions of 2n with at least n 1's and ; 1 , ..., ; k be partitions of 2n with exactly n parts. By M n we denote the matrix whose entries m ij are the number of ways to refine ; j into : i . It is shown that det M n =1 for all n. 1996 Academic Press, Inc. ## 1. Introduction
Let Zm be the ring of integers modulo m. The m-rank of an integer matrix is the largest order of a square submatrix whose determinant is not divisible by m. We determine the probability that a random rectangular matrix over ~Ym has a specified m-rank and, if it is square, a specified determinant. Th