HP Labs Technical Reports
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Resummation and the Turning Points of Zeta Functions
Keating, J.P.
HPLBRIMS9627
Keyword(s): semiclassical quantization; RiemannSiegel resummation; zetafunctions
Abstract: We review various periodic orbit formulae for the zeta function whose zeros represent semiclassical approximations to the energy levels of chaotic systems. In particular, we focus on the RiemannSiegel resummed expression. The emphasis is on the ability of such formulae to reproduce the analytic properties of the spectral determinant, whose zeros are the exact quantum levels. As an example, the distribution of turning points is investigated and compared.
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