##  [Zeta-Regularized Determinant](/index.php/zeta-regularized-determinant) 

  ##  [Zeta-Regularized Determinant](https://puremath.quantumdictionary.io/zeta-regularized-determinant-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A definition of a determinant for elliptic (typically positive) operators via the spectral zeta function: if {λ_j} are the positive eigenvalues, form ζ(s) = ∑ λ_j^{-s}, analytically continue ζ(s) to s=0 and define det' A = exp(−ζ'(0)). This regularizes the divergent infinite product of eigenvalues and produces meaningful spectral invariants.