Hamiltonians arising from L-functions in the Selberg class

  title={Hamiltonians arising from L-functions in the Selberg class},
  author={Masatoshi Suzuki},
  journal={arXiv: Number Theory},
We establish a new equivalent condition for the Grand Riemann Hypothesis for L-functions in a wide subclass of the Selberg class in terms of canonical systems of differential equations. A canonical system is determined by a real symmetric matrix valued function called a Hamiltonian. To establish the equivalent condition, we solve and use an inverse spectral problem for canonical systems of special type. 
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