A. A. Agrachev and Y. L. Sachkov, Control Theory from the Geometric Viewpoint, 2004.

P. Albin, C. L. Aldana, and F. Rochon, Ricci flow and the determinant of the Laplacian on non-compact surfaces, Comm. Partial Differential Equations, vol.38, pp.711-749, 2013.

E. Aurell and P. Salomonson, On functional determinants of Laplacians in polygons and simplicial complexes, Comm. Math. Phys, vol.165, pp.233-259, 1994.

B. Bonnard and M. Chyba, Singular trajectories and their role in control theory, 2003.

D. Burghelea, L. Friedlander, and T. Kappeler, On the determinant of elliptic boundary value problems on a line segment, Proc. Amer. Math. Soc, vol.123, pp.3027-3038, 1995.

L. Cesari, , 1983.

E. A. Coddington and N. Levinson, Theory of ordinary differential equations, 1955.

P. Freitas, The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions, Math. Ann, vol.372, pp.1081-1101, 2018.

I. M. Gelfand and A. M. Yaglom, Integration in functional spaces and it applications in quantum physics, J. Math. Phys, vol.1, pp.48-69, 1960.

E. M. Harrell, Hamiltonian operators with maximal eigenvalues, J. Math. Phys, vol.25, pp.48-51, 1984.

. Erratum, J. Math. Phys, vol.27, p.419, 1986.

T. Kato, Perturbation Theory for Linear Operators, 1995.

M. Lesch, Determinants of regular singular Sturm-Liouville operators, Math. Nachr, vol.194, pp.139-170, 1998.

M. Lesch and J. Tolksdorf, On the determinant of one-dimensional elliptic boundary value problems, Comm. Math. Phys, vol.193, pp.643-660, 1998.

S. Levit and U. Smilansky, A theorem of infnite products of eigenvalues of Sturm-Liouville type operators, Proc. Amer. Math. Soc, vol.65, pp.299-302, 1977.

S. Minakshisundaram, Some properties of the eigenfunctions of the Laplaceoperator on Riemannian manifolds, Canadian J. Math, vol.1, pp.242-256, 1949.

B. Osgood, R. Phillips, R. , and P. Sarnak, Extremals of determinants of Laplacians, J Funct. Anal, vol.80, pp.148-211, 1988.

D. B. Ray and I. M. Singer, R-torsion and the Laplacian on Riemannian manifolds, Adv. Math, vol.7, pp.145-210, 1971.

B. Riemann, Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse, English translation in H.M. Edwards, Riemanns zeta function, pp.671-680, 1859.

E. C. Titchmarsh, The theory of the Riemann zeta function, 1988.

A. M. , Savchuk On the eigenvalues and eigenfunctions of the Sturm-Liouville operator with a singular potential, Math. Notes, vol.69, pp.277-285, 2001.

A. M. Savchuk and A. A. Shkalikov, Sturm-Liouville operators with singular potentials, Math. Notes, vol.66, pp.741-753, 1999.

, Vía Puerto Colombia, Barranquilla, Colombia E-mail address: claldana@uninorte