Random matrices and Riemann hypothesis

Details Random matrices and Riemann hypothesis Random matrices and Riemann hypothesis

2011-09-22

arxiv.org/abs/1109.5586v1

Mathematics

General Mathematics

74 pages

Scientific paper

The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of Langlands whose fundamental structures are shifted quantized conjugacy class representatives of bilinear algebraic semigroups.The considered symmetry behind this phenomenology is the differential bilinear Galois semigroup shifting the product,right by left,of automorphism semigroups of cofunctions and functions on compact transcendental quanta.

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