Hamiltonians arising from L-functions in the Selberg class

Abstract

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 matrixvalued function called a Hamiltonian. To establish the equivalent condition, we use an inverse problem for canonical systems of a special type.

The paper has been significantly revised, because a part of the old version was published as the reference [45] of the latest version

References in corpus (2)

• L-functions as distributions
• On monotonicity of certain weighted summatory functions associated with L-functions

Cited by in corpus (1)

• Integral operators arising from the Riemann zeta function