Symmetric matrices related to the Mertens function

Details Symmetric matrices related to the Mertens function Symmetric matrices related to the Mertens function

2008-11-22

arxiv.org/abs/0811.3701v4

Mathematics

Number Theory

Version submitted to LAA; some new references

Scientific paper

In this paper we explore a family of congruences over $\N^\ast$ from which one builds a sequence of symmetric matrices related to the Mertens function. From the results of numerical experiments, we formulate a conjecture about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may come to play a more important role in this classical and difficult problem.

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