
#1
Oct1310, 01:22 AM

P: 499

In "A Prime Case of Chaos" (http://www.ams.org/samplings/mathhi...rimechaos.pdf), the author states that "Physicists ... believe the zeroes of the zeta function can be interpreted as energy levels...." I have two problems with this:
(1) the nontrivial zeroes of the zeta function are complex numbers, and energy levels, such as the Ryberg formula, are real numbers. So how could you interpret something like (1/2) + (14.134725)i as an energy level? (2) the three dots in the above quote say that this is tied to the zeta function being a trace formula. Following this lead, the best my very limited background in the mathematics needed for this physics could come up with, was in "Selberg trace formula and zeta functions" at http://empslocal.ex.ac.uk/people/sta...a/physics4.htm, where it explains: "Selberg trace formula .... relates ... the spectrum of the quantal motion on compact surfaces of negative curvature ...; however, it does not address itself ...to ... the detailed properties of the discrete energy spectrum ..." which led me to a dead end in trying to answer my question (1), although that may be due to my limited grasp of what the formula is saying. If a response gives any sources, could they please be online sources that are freely accessible? If this should go in some other category, please let me know. I put it here because of the connection to the Riemann Hypothesis. Thanks for any help. 


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