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

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

2003-03-12

arxiv.org/abs/math-ph/0303030v3

J.Phys.A36:9991-10010,2003

Physics

Mathematical Physics

26 pages, 1 figure, LaTeX. References added. Version to appear in the Journal of Physics A: Math. and Gen

Scientific paper

10.1088/0305-4470/36/39/302

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 $\lambda$ which depend on the singularity, and can take even irrational values. The consequences for the pole structure of the corresponding $\zeta$ and $\eta$-functions are also discussed.

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