Hamiltonians for the zeros of a general family of zeta functions

Abstract

Towards the Hilbert-Pólya conjecture, in this paper, we present a general construction of Hamiltonian ${\hat{H}}_f,$ which leads a general family of Hurwitz zeta functions $(-1{)}^{z_n-1}L(f,z_n,x+1)$ defined by Mellin transform becomes their eigenstates under a suitable boundary condition, and the eigenvalues $E_n$ have the property that $z_n=\frac{1}{2}(1-i{E}_n)$ are the zeros of a general family of zeta functions $L(f,z)\equiv L(f,z,1)$.

Comments are welcome

References in corpus (1)

• Hamiltonian for the zeros of the Riemann zeta function