Mathematical Physics

   

A Functional Determinant Expression for the Riemann XI Function

Authors: Jose Javier Garcia Moreta

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos.

Comments: 13 Pages.

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Submission history

[v1] 2012-06-19 15:01:49
[v2] 2012-06-25 04:35:14
[v3] 2012-07-06 06:09:46
[v4] 2012-08-26 07:01:41
[v5] 2012-09-26 14:59:59

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