Abstract
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.
Ferguson, R; Hoffman, C; Luca, F; Ostafe, A; Shparlinski, I E (2010). Some additive combinatorics problems in matrix rings. Revista matematica complutense, 23(2):501-513.
Abstract
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.
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| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Language: | English |
| Date: | July 2010 |
| Deposited On: | 16 Aug 2010 14:37 |
| Last Modified: | 28 Jun 2022 10:22 |
| Publisher: | Springer |
| ISSN: | 1139-1138 |
| Additional Information: | The original publication is available at www.springerlink.com |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/s13163-010-0029-4 |
| Related URLs: | http://arxiv.org/abs/0902.3482 |
| Other Identification Number: | arXiv:0902.3482v2 |
Ferguson, R