STATISTICS OF PRIME DIVISORS IN FUNCTION FIELDS
- RHOADES, ROBERT C. Department of Mathematics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- 2011-11-21
Published in:
- International Journal of Number Theory. - World Scientific Pub Co Pte Lt. - 2009, vol. 05, no. 01, p. 141-152
English
We show that the prime divisors of a random polynomial in 𝔽q [t] are typically "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–Kac theorem in the function field setting. This approach gives stronger results about the moments of the sequence {ω(f)}f∈𝔽q [t] than was previously known, where ω(f) is the number of prime divisors of f.
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1142/s1793042109001980
- ISSN 1793-0421
- Persistent URL
- https://sonar.ch/global/documents/130229
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