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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184580We 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.26 pages, 1 figure, LaTeX. References added. Version to appear in the Journal of Physics A: Math. and GenMathematical PhysicsHigh Energy Physics - TheoryFunctional AnalysisQuantum Physics81Q10, 34L05, 34L40Unusual poles of the $ζ$-functions for some regular singular differential operatorstext