Integer matrices related to Liouville's function
Czechoslovak Mathematical Journal (2013)
- Volume: 63, Issue: 1, page 39-46
- ISSN: 0011-4642
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topOon, Shea-Ming. "Integer matrices related to Liouville's function." Czechoslovak Mathematical Journal 63.1 (2013): 39-46. <http://eudml.org/doc/252544>.
@article{Oon2013,
abstract = {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.},
author = {Oon, Shea-Ming},
journal = {Czechoslovak Mathematical Journal},
keywords = {Liouville's function; determinant; LU decomposition; Liouville's function; determinant; LU decomposition},
language = {eng},
number = {1},
pages = {39-46},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Integer matrices related to Liouville's function},
url = {http://eudml.org/doc/252544},
volume = {63},
year = {2013},
}
TY - JOUR
AU - Oon, Shea-Ming
TI - Integer matrices related to Liouville's function
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 39
EP - 46
AB - 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.
LA - eng
KW - Liouville's function; determinant; LU decomposition; Liouville's function; determinant; LU decomposition
UR - http://eudml.org/doc/252544
ER -
References
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