##  [Zeta-Function Regularization](/zeta-function-regularization) 

  ##  [Zeta-Function Regularization](https://mathlogic.quantumdictionary.io/zeta-function-regularization-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A method for assigning finite values to divergent spectral sums or infinite products by forming an associated zeta function ζ(s) (typically ζ(s)=∑ λ_i^{-s} for positive eigenvalues λ_i), analytically continuing ζ(s) to a neighborhood of a special point (often s=0), and defining regularized sums or determinants via values like ζ(0) or derivatives such as -ζ'(0).