A Carlitz module analogue of a conjecture of Erdos and Pomerance
| dc.contributor.author | Kuo, Wentang | |
| dc.contributor.author | Liu, Yu-Ru | |
| dc.date.accessioned | 2023-10-03T15:08:58Z | |
| dc.date.available | 2023-10-03T15:08:58Z | |
| dc.date.issued | 2009-09 | |
| dc.description.abstract | Abstract. Let A = Fq[T] be the ring of polynomials over the finite field Fq and 0 = a ∈ A. Let C be the A-Carlitz module. For a monic polynomial m ∈ A, let C(A/mA) and ¯a be the reductions of C and a modulo mA respectively. Let fa(m) be the monic generator of the ideal {f ∈ A, Cf (¯a) = ¯0} on C(A/mA). We denote by ω(fa(m)) the number of distinct monic irreducible factors of fa(m). If q = 2 or q = 2 and a = 1, T, or (1 + T), we prove that there exists a normal distribution for the quantity ω(fa(m)) − 1 2 (log deg m)2 √1 3 (log deg m)3/2 . This result is analogous to an open conjecture of Erd˝os and Pomerance concerning the distribution of the number of distinct prime divisors of the multiplicative order of b modulo n, where b is an integer with |b| > 1, and n a positive integer. | en |
| dc.identifier.uri | https://doi.org/10.1090/s0002-9947-09-04723-0 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19996 | |
| dc.language.iso | en | en |
| dc.publisher | American Mathematical Society | en |
| dc.relation.ispartofseries | Transactions of the American Mathematical Society;361(9) | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.title | A Carlitz module analogue of a conjecture of Erdos and Pomerance | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Kuo, W., & Liu, Y.-R. (2009). A Carlitz module analogue of a conjecture of Erdos and pomerance. Transactions of the American Mathematical Society, 361(9), 4519–4539. https://doi.org/10.1090/s0002-9947-09-04723-0 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |