Hamiltonians arising from L-functions in the Selberg class

摘要

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 use an inverse problem for canonical systems of a special type. (C) 2021 The Author(s). Published by Elsevier Inc.