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arXiv · 1810.11662

Hamiltonians for the zeros of a general family of zeta functions

Su Hu·Min-Soo Kim
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Abstract

Towards the Hilbert-P\'olya 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 $z_{n}=\frac{1}{2}(1-iE_{n})$ are the zeros of a general family of zeta functions $L(f,z)\equiv L(f,z,1)$.

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Su Hu, Min-Soo Kim. 2018-10-27. Hamiltonians for the zeros of a general family of zeta functions. https://arxiv.org/abs/1810.11662

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