Affiliation:
1. Department of Mathematics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Reference5 articles.
1. PRIME DIVISORS ARE POISSON DISTRIBUTED
2. A. Granville and K. Soundararajan, Equidistribution in Number Theory, An Introduction, eds. A. Granville and Z. Rudnick (Springer, 2007) pp. 15–27.
3. A Generalization of the Erdös-Kac Theorem and its Applications
4. Number Theory in Function Fields
5. W.B. Zhang, Analytic Number Theory, Vol 2, Progress in Mathematics 139, eds. B. Berndt and et al (Birkhauser, Boston, MA, 1995) pp. 839–885.
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