{rfName}
DI

Indexed in

License and use

Citations

Altmetrics

Grant support

The first author is partially supported by the grant MTM2011-22851 from the Ministerio de Ciencia e Innovacion (Spain).

Analysis of institutional authors

Raboso, DulcineaAuthor

Share

May 14, 2025
Publications
>
Article
No

DISTRIBUTIONAL PROPERTIES OF POWERS OF MATRICES

Publicated to:Czechoslovak Mathematical Journal. 64 (3): 801-817 - 2014-09-01 64(3), DOI: 10.1007/s10587-014-0133-6

Authors: Chamizo, Fernando; Raboso, Dulcinea

Affiliations

Univ Autonoma Madrid, Fac Sci, Dept Math, E-28049 Madrid, Spain - Author
Univ Autonoma Madrid, Fac Sci, ICMAT, E-28049 Madrid, Spain - Author

Abstract

We apply the larger sieve to bound the number of 2x2 matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar matrices having large order. In this direction we find matrices of large order when the trace is restricted to take values in a short interval.

Keywords

Artins conjectureConsecutive primesDifferencFinite fieldGeneral linear group of degreeGeneratorsLarger sievePrimitive rootsPseudorandom numberSpecial linear group of degree 2

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Czechoslovak Mathematical Journal, and although the journal is classified in the quartile Q4 (Agencia WoS (JCR)), its regional focus and specialization in Mathematics, give it significant recognition in a specific niche of scientific knowledge at an international level.

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-08-13:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (Raboso Paniagua, Dulcinea).