Statistics of Prime Divisors in Function Fields

  title={Statistics of Prime Divisors in Function Fields},
  author={ROBERT C. RHOADESproblem},
  • ROBERT C. RHOADESproblem
  • Published 2007
ROBERT C. RHOADES Abstra t. We show that the prime divisors of a random polynomial in Fq[t] are typi ally Poisson Distributed . This result is analogous to the result in Z of Granville [1℄. Along the way, we use a sieve developed by Granville and Soundararajan [2℄ to give a simple proof of the Erdös-Ka theorem in the fun tion eld setting. This approa h gives stronger results about the moments of the sequen e {ω(f)}f∈Fq [t] than was previously known, where ω(f) is the number of prime divisors of… CONTINUE READING

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A Generalization of the ErdösKa Theorem and its Appli ations

  • A. Granville, K. Soundararajan
  • Canad . Math . Bull .
  • 2007

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