44 research outputs found
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
The Riemann zeros as spectrum and the Riemann hypothesis
We present a spectral realization of the Riemann zeros based on the
propagation of a massless Dirac fermion in a region of Rindler spacetime and
under the action of delta function potentials localized on the square free
integers. The corresponding Hamiltonian admits a self-adjoint extension that is
tuned to the phase of the zeta function, on the critical line, in order to
obtain the Riemann zeros as bound states. The model suggests a proof of the
Riemann hypothesis in the limit where the potentials vanish. Finally, we
propose an interferometer that may yield an experimental observation of the
Riemann zeros.Comment: 33 pages, 17 figures, new abstract, simplification of several
sections, changes of reference