##  [Tamagawa Number](/tamagawa-number) 

  ##  [Tamagawa Number](https://puremath.quantumdictionary.io/tamagawa-number-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An arithmetic invariant of a connected algebraic group or abelian variety over a global field defined as the volume of the adelic quotient G(A)/G(K) with respect to a canonical Tamagawa measure; it measures the defect of naive product-of-local-volumes formulas and appears in arithmetic formulas relating local and global points.