The Residue Determinant

DOI10.1081/PDE-200050102zbMath1236.58037arXivmath/0406268MaRDI QIDQ5314599

Simon G. Scott

Publication date: 5 September 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406268

zbMATH Keywords

determinantzetamultiplicativeresidue trace

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Determinants and determinant bundles, analytic torsion (58J52) Pseudodifferential operators (47G30) First-order elliptic systems (35J46)

Related Items (9)

The local counting function of operators of Dirac and Laplace type ⋮ Uniqueness of multiplicative determinants on elliptic pseudodifferential operators ⋮ The multiplicative anomaly for determinants revisited; locality ⋮ On the Logarithm Component in Trace Defect Formulas ⋮ THE LOGARITHMIC RESIDUE DENSITY OF A GENERALIZED LAPLACIAN ⋮ Residue-torsion and the Laplacian on Riemannian manifolds ⋮ On the topology of the space of invertible pseudodifferential operators of order 0 ⋮ Determinants of classical SG‐pseudodifferential operators ⋮ SPECTRAL ASYMMETRY, ZETA FUNCTIONS, AND THE NONCOMMUTATIVE RESIDUE

Cites Work

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• Local invariants of spectral asymmetry
• Spectral asymmetry and zeta functions
• Relative zeta functions, relative determinants and scattering theory
• Conformal geometry and global invariants
• Gauged Lagrangian distributions
• Zeta determinants on manifolds with boundary
• Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
• The Campbell-Hausdorff theorem for elliptic operators and a related trace formula
• The multiplicative anomaly for determinants of elliptic operators
• A Laurent expansion for regularized integrals of holomorphic symbols
• On the Logarithm Component in Trace Defect Formulas

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