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A new short proof of Naranan's theorem, explaining Lotka's law and Zipf's law

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  • Leo Egghe

Abstract

Naranan's important theorem, published in Nature in 1970, states that if the number of journals grows exponentially and if the number of articles in each journal grows exponentially (at the same rate for each journal), then the system satisfies Lotka's law and a formula for the Lotka's exponent is given in function of the growth rates of the journals and the articles. This brief communication re‐proves this result by showing that the system satisfies Zipf's law, which is equivalent with Lotka's law. The proof is short and algebraic and does not use infinitesimal arguments.

Suggested Citation

  • Leo Egghe, 2010. "A new short proof of Naranan's theorem, explaining Lotka's law and Zipf's law," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 61(12), pages 2581-2583, December.
    • Handle: RePEc:bla:jamist:v:61:y:2010:i:12:p:2581-2583
    DOI: 10.1002/asi.21431
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