Cremona, J. E. (2008) Unimodular integer circulants. Mathematics of Computation, Vol.77 (No.263). pp. 1639-1652. doi:10.1090/S0025-5718-08-02089-9 ISSN 0025-5718.

Research output not available from this repository.

Request-a-Copy directly from author or use local Library Get it For Me service.

Request Changes to record.

Abstract

We study families of integer circulant matrices and methods for determining which are unimodular. This problem arises in the study of cyclically presented groups, and leads to the following problem concerning polynomials with integer coefficients: given a polynomial f(x) is an element of Z[x], determine all those n is an element of N such that Res(f(x), x(n) - 1) = +/-1. In this paper we describe methods for resolving this problem, including a method based on the use of Strassman's Theorem on p-adic power series, which are effective in many cases. The methods are illustrated with examples arising in the study of cyclically presented groups and further examples which illustrate the strengths and weaknesses of the methods for polynomials of higher degree.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Matrices, Toeplitz matrices
Journal or Publication Title:	Mathematics of Computation
Publisher:	American Mathematical Society
ISSN:	0025-5718
Official Date:	2008
Dates:	Date Event 2008 Published
Volume:	Vol.77
Number:	No.263
Number of Pages:	14
Page Range:	pp. 1639-1652
DOI:	10.1090/S0025-5718-08-02089-9
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

Data sourced from Thomson Reuters' Web of Knowledge

Request changes or add full text files to a record

Repository staff actions (login required)

View Item