The spectral determinant associated with an elliptic operator may be defined via the corresponding zeta function. We have been concerned with finding explicit formulas for determinants, including for the n-dimensional harmonic oscillator [F18,FC25], Sturm-Liouville operators on the whole line [FL24], polyharmonic operators [FL20]. and the Laplacian on spheres, hemispheres, and projective spaces [FC25]. In [F18,FC25], we've shown how to use recurrence relations in the space dimension to compute the determinant in an efiicient way. In another direction, we've studied extremal values of the determinant, particularly for Sturm-Liouville operators on bounded intervals [ACF19] and on the circle [CCFP24].
[ACF20] Maximal determinants of Schrödinger operators on bounded intervals. J. Éc. polytech. Math. 7 (2020), 803–829 (with Clara Aldana and Jean-Baptiste Caillau).
[CCFP24] Optimisation of functional determinants on the circle. In Ivan Kupka Legacy, A Tour Through Controlled Dynamics, AIMS on Applied Mathematics 12 (2024), 155–171 (with Jean-Baptiste Caillau, Yacine Chitour and Yannick Privat).
[F18] The spectral determinant of the isotropic quantum harmonic oscillator in arbitrary dimensions. Math. Ann. 372 (2018), 1081–1101.
[FC25] Recurrence formulae for spectral determinants. J. Number Theory 267 (2025), 134–175 (with José Cunha).
[FL24] The spectral determinant for second order elliptic operators on the real line. Lett. Math. Phys. 114:65 (2024), 17pp (with Jiří Lipovský).
[FL20] The determinant of one-dimensional polyharmonic operators of arbitrary order. J. Funct. Anal. 279 (2020), 108783, 30pp (with Jiří Lipovský).
[FL19] Spectral determinant for the damped wave equation on an interval. Acta Phys. Polon. A 136 (2019), 817–823 (with Jiří Lipovský).