Some experiments on the growth of Mertens matrices
Jean-Paul Cardinal
TL;DR
This paper presents experimental observations on the growth of Mertens-related matrices, suggesting linear algebra could be a useful tool in understanding the Mertens function and similar arithmetic functions.
Contribution
It introduces experimental analysis of Mertens matrices growth, proposing a new approach using linear algebra in number theory research.
Findings
Matrices related to Mertens function show specific growth patterns
Linear algebra techniques may aid in studying arithmetic functions
Experimental results support potential theoretical developments
Abstract
We give some experimental observations on the growth of the norm of certain matrices related to the Mertens function. The results obtained in these experiments convince us that linear algebra may help in the study of Mertens function and other arithmetic functions.
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Taxonomy
TopicsMatrix Theory and Algorithms · Meromorphic and Entire Functions · Advanced Mathematical Theories and Applications