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Unusual poles of the $ζ$-functions for some regular singular differential operators

H. Falomir·M. A. Muschietti·P. A. G. Pisani·R. Seeley
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Abstract

We consider the resolvent of a system of first order differential operators with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents powers of $λ$ which depend on the singularity, and can take even irrational values. The consequences for the pole structure of the corresponding $ζ$ and $η$-functions are also discussed.

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H. Falomir, M. A. Muschietti, P. A. G. Pisani, R. Seeley. 2003-09-05. Unusual poles of the $ζ$-functions for some regular singular differential operators. https://doi.org/10.1088/0305-4470/36/39/302

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