An Elementary Problem Equivalent to the Riemann Hypothesis

  title={An Elementary Problem Equivalent to the Riemann Hypothesis},
  author={Jeffrey C. Lagarias},
  journal={The American Mathematical Monthly},
  pages={534 - 543}
  • J. Lagarias
  • Published 22 August 2000
  • Mathematics
  • The American Mathematical Monthly
The function a (n) = dInd is the sum-of-divisors function, so for example a (6) = 12. The number Hn is called the nth harmonic number by Knuth, Graham, and Patashnik [12, sect. 6.3], who detail various properties of harmonic numbers. The 'E' in Problem E might stand for either 'easy' or 'elementary'. Perhaps 'H' for 'hard' would be a better letter to use, since our object is to show the following equivalence. 
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