Ten years ago the speaker reformulated the Riemann Hypothesis as statements about the eigenvalues of certain

Hankel matrices, entries of which are defined via the Taylor series coefficients of the zeta function. Numerical

calculations revealed some very interesting visual patterns in the behaviour of the eigenvalues and allowed the

speaker to state a number of new conjectures related to the Riemann Hypothesis.

Recently computations have been performed on more powerful computers. This led to new conjectures about

the finer structure of the eigenvalues and eigenvectors and to conjectures that are (formally) stronger than

the Riemann Hypothesis.

More information can be found at {\url{http://logic.pdmi.ras.ru/~yumat/personaljournal/zetahiddenlife}}

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