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Spectral Zeta Functions

Paul Abbott
Organization: University of Western Australia
Department: Physics
URL: http://www.uwa.edu.au/people/paul.c.abbott

Wolfram Technology Conference 2014
Conference location

Champaign, Illinois, USA

When the eigenvalues of an operator A can be computed and form a discrete set the spectral zeta function of A reduces to a sum over eigenvalues, when the sum exists (see Berry [1], Elizalde [2], and Crandall [3]). Belloni and Robinett [4] used the “quantum bouncer” to compute quantum sum rules (see Vallée and Soares [5]). Here we use Mathematica to compute the spectral zeta function for various special functions via the Weierstrass product theorem.


[1] Berry M V 1986 “Spectral zeta functions for Aharonov-Bohm quantum billiards” J. Phys. A: Math. Gen. 19 2281-96 [2] Elizalde E 1995 Ten physical applications of spectral zeta functions (Berlin: Springer) [3] Crandall R E 1996 “On the quantum zeta function” J. Phys. A: Math. Gen. 29 6795-6816 [4] Belloni M and Robinett R W 2009 “Constraints on Airy function zeros from quantum-mechanical sum rules” J. Phys. A 42 075203 [5] Vallée O and Soares M 2004 Airy functions and applications to physics (London: Imperial College Press)

*Wolfram Technology


WTC14SpectralZeta_PaulAbbot.cdf (2.6 MB) - CDF Document