##  [Explicit Formula (Prime Number Theory)](/explicit-formula-prime-number-theory) 

  ##  [Explicit Formula (Prime Number Theory)](https://puremath.quantumdictionary.io/explicit-formula-prime-number-theory-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An analytic identity that relates sums over prime powers (or weighted prime-counting functions) to explicit sums over the nontrivial zeros of L-functions, making precise how prime distribution is encoded in spectral data of zeta or L-functions.