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.
- Pub Date:
- June 2016
- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Functional Analysis;
- The paper has been significantly revised, because a part of the old version was published as the reference  of the latest version