Eigenvalues and eigenvectors of some Hankel matrices related to the zeta and L-functions

talk given by Yuri Matiyasevich  at   Analytic Number Theory Workshop   in   Turku, Finland on May 28, 2014

Abstract.  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.

Original slides   .pdf (2.4Mb)

Slides for printing   .pdf (2.3MB)

Animation  .pdf (1.8MB)

Voice recording   .mp3 (27Mb)  

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