3 fixed a few typos

the Xi fucntion appear function appears as the funcitonal determiant functional determinant $\frac{ \xi(s)}{\xi(0)}= \frac{det(H+s(s-1)+1/4)}{det(H+1/4)}$ of a certian certain Hamiltonian with the potential $V^{-1}(x)= A \sqrt D n(x)$

with $n(x) \pi = Arg\xi (1/2+ i \sqrt x)$

here 'n' plays the role of Eigenvalue staircase $n(x)= \sum_{n=0}^{\infty}H(x-E_{n})$ and 'H(x)' is the Heaviside function.

2 added 128 characters in body

the Xi fucntion appear as the funcitonal determiant $\frac{ \xi(s)}{\xi(0)}= \frac{det(H+s(s-1)+1/4)}{det(H+1/4)}$ of a certian Hamiltonian with the potential $V^{-1}(x)= A \sqrt D n(x)$

with $N(xn(x) \pi = Arg\xi (1/2+ i \sqrt x)$

here 'n' plays the role of Eigenvalue staircase $n(x)= \sum_{n=0}^{\infty}H(x-E_{n})$ and 'H(x)' is the Heaviside function.

1

the Xi fucntion appear as the funcitonal determiant $\frac{ \xi(s)}{\xi(0)}= \frac{det(H+s(s-1)+1/4)}{det(H+1/4)}$ of a certian Hamiltonian with the potential $V^{-1}(x)= A \sqrt D n(x)$

with $N(x) \pi = Arg\xi (1/2+ i \sqrt x)$