Determinants of the Laplacians on complex projective spaces \(\mathbf{P}^n(\mathbb{C})(n\geq 1)\)
From MaRDI portal
Publication:1753819
DOI10.1016/j.jnt.2018.02.007zbMath1404.33005OpenAlexW2792425398MaRDI QIDQ1753819
Publication date: 29 May 2018
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jnt.2018.02.007
complex projective spacespectral zeta functiondeterminant of LaplacianMinakshisundaram-Pleijel coefficients
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Fundamental solutions to PDEs (35A08) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Solutions to PDEs in closed form (35C05)
Related Items
Maclaurin spectral results on rank one symmetric spaces of noncompact type ⋮ Functional determinant of Laplacian on Cayley projective plane \(\mathbf{P}^{2}(\text{Cay})\) ⋮ Spectral \(\zeta\)-functions and \(\zeta\)-regularized functional determinants for regular Sturm-Liouville operators ⋮ On the spectral zeta functions of the Laplacians on the projective complex spaces and on the \(n\)-spheres ⋮ On Jacobi polynomials and fractional spectral functions on compact symmetric spaces
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten
- Determinants of Laplacians
- Sums of certain series of the Riemann zeta function
- Extremals of determinants of Laplacians
- Determinants of Laplacians on surfaces of finite volume
- Topics in harmonic analysis on homogeneous spaces
- A new proof of a Paley-Wiener type theorem for the Jacobi transform
- Eigenspaces of the Laplacian ; integral representations and irreducibility
- Zeta functions and their asymptotic expansions for compact symmetric spaces of rank one
- Certain classes of series involving the zeta function
- Nonlinear elliptic equations in conformal geometry
- Extremal metrics of zeta function determinants on 4-manifolds
- Zeta function determinant of the Laplace operator on the \(D\)-dimensional ball
- On Jacobi polynomials \((\mathcal {P}_k^{(\alpha, \beta)}: \alpha, \beta >-1)\) and Maclaurin spectral functions on rank one symmetric spaces
- The spectral function of an elliptic operator
- Curvature and the eigenvalues of the Laplacian
- Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
- R-torsion and the Laplacian on Riemannian manifolds
- Analytic torsion for complex manifolds
- Determinant Expression of Selberg Zeta Functions. I
- Determinants of Laplacians and Multiple Gamma Functions
- Explicit Functional Determinants in Four Dimensions
- Determinant Expression of Selberg Zeta Functions. II
- Some series of the zeta and related functions
- AN APPLICATION OF THE THEORY OF THE DOUBLE GAMMA FUNCTION
- The Functional Determinant of a Four-Dimensional Boundary Value Problem
- Functional determinants on spheres and sectors
- The determinant of the Laplacian on the n-sphere
- Analysis and Geometry of Markov Diffusion Operators
- Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
- Geometric Analysis
- Spectral zeta functions for compact symmetric spaces of rank one
- Critical metrics for the determinant of the Laplacian in odd dimensions
