Proving ζ(-1)=-1/12 for Mathematicians

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SUMMARY

The equation ζ(-1) = -1/12 is proven through the proper definition of the zeta function for negative integers. The discussion highlights that once the zeta function is appropriately defined, the proof becomes straightforward. A recommended resource for a detailed proof is the book by Godement, specifically Chapter VI.2.19.

PREREQUISITES
  • Understanding of the Riemann zeta function
  • Familiarity with analytic continuation
  • Knowledge of complex analysis
  • Basic concepts of number theory
NEXT STEPS
  • Study the Riemann zeta function and its properties
  • Explore analytic continuation techniques
  • Read Godement's book on the zeta function for detailed proofs
  • Investigate applications of ζ(-1) in number theory
USEFUL FOR

Mathematicians, students of number theory, and anyone interested in advanced mathematical concepts related to the Riemann zeta function.

moriheru
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How can one prove the above equation?
Thanks.
 
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Thanks micromass!
 

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