The zeta functions for the Schr\”odinger equation with a triangular potential
    are investigated. Values of the zeta functions are computed using both the
    Weierstrass factorization theorem and analytic continuation via contour
    integration. The results were found to be consistent where the domains of the
    two methods overlap. Analytic continuation is used to compute values of the
    zeta functions at zero and the negative integers, explore the pole structure
    (and residue values), as well as the value of the slopes at the origin. Those
    results are used for the computation of the trace and determinant of the
    associated Hamiltonians.

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