The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions

  title={The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions},
  author={Paul Erd{\"o}s and Mark Kac},
  journal={American Journal of Mathematics},
The present paper concerns itself with the applications of statistical methods to some number-theoretic problems. Recent inrestigations of Erdiis and Wintrier ? have shown the importance of the notion of statistical independence in number theory ; the purpose of this paper is to emphasize this fact once again. It may be mentioned here that we get as a particular case of our main theorem the following result : If v(m) denotes the number of prime divisors of ~1, and En the number of those… 
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