Eigenvalues and eigenvectors of some Hankel matrices
related to the zeta and L-functions
In 2007 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 has been extended to Dirichlet L-functions and were performed on more
powerful computers. This led to new conjectures about the finer structure of
the eigenvalues and eigenvectors, about non-evident relations among Taylor coefficients
of the zeta and L-functions and to conjectures that are (formally) stronger than RH.