A new example of the effects of a singular background on the zeta function

@article{Falomir2020ANE,
  title={A new example of the effects of a singular background on the zeta function},
  author={Horacio Falomir and Joaquin Liniado and Pablo A. G. Pisani},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
To motivate our discussion, we consider a 1+1 dimensional scalar field interacting with a static Coulomb-type background, so that the spectrum of quantum fluctuations is given by a second-order differential operator on a single coordinate r with a singular coefficient proportional to 1/r. We find that the spectral functions of this operator present an interesting behavior: the zeta function has multiple poles in the complex plane; accordingly, logarithms of the proper time appear in the heat… 

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