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.
