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Title: Integer matrices related to Liouville's function (English)
Author: Oon, Shea-Ming
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 63
Issue: 1
Year: 2013
Pages: 39-46
Summary lang: English
Category: math
Summary: In this note, we construct some integer matrices with determinant equal to certain summation form of Liouville's function. Hence, it offers a possible alternative way to explore the Prime Number Theorem by means of inequalities related to matrices, provided a better estimate on the relation between the determinant of a matrix and other information such as its eigenvalues is known. Besides, we also provide some comparisons on the estimate of the lower bound of the smallest singular value. Such discussion may be extended to that of Riemann hypothesis. (English)
Keyword: Liouville's function
Keyword: determinant
Keyword: LU decomposition
MSC: 11A25
MSC: 11C20
MSC: 15A15
MSC: 15B36
idZBL: Zbl 1274.11012
idMR: MR3035495
DOI: 10.1007/s10587-013-0002-8
Date available: 2013-03-01T16:00:47Z
Last updated: 2020-07-03
Stable URL:
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