Hamiltonians arising from L-functions in the Selberg class
Number Theory
2020-10-02 v3 Classical Analysis and ODEs
Functional Analysis
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.
Keywords
Cite
@article{arxiv.1606.05726,
title = {Hamiltonians arising from L-functions in the Selberg class},
author = {Masatoshi Suzuki},
journal= {arXiv preprint arXiv:1606.05726},
year = {2020}
}
Comments
The paper has been significantly revised, because a part of the old version was published as the reference [45] of the latest version