Notes on Cardinal's Matrices
Number Theory
2015-11-26 v1 Rings and Algebras
Abstract
These notes are motivated by the work of Jean-Paul Cardinal on symmetric matrices related to the Mertens function. He showed that certain norm bounds on his matrices implied the Riemann hypothesis. Using a different matrix norm we show an equivalence of the Riemann hypothesis to suitable norm bounds on his matrices in the new norm. Then we specify a deformed version of his Mertens function matrices that unconditionally satisfies a norm bound that is of the same strength as his Riemann hypothesis bound.
Cite
@article{arxiv.1511.08154,
title = {Notes on Cardinal's Matrices},
author = {Jeffrey C. Lagarias and David Montague},
journal= {arXiv preprint arXiv:1511.08154},
year = {2015}
}
Comments
21 pages