Author
Gorodetsky, O
Journal title
Finite Fields and Their Applications
DOI
10.1016/j.ffa.2018.12.002
Volume
56
Last updated
2024-03-24T21:51:22.167+00:00
Page
150-187
Abstract
For any positive integers n ≥ 3 and r ≥ 1, we prove that the number of monic irreducible
polynomials of degree n over F2r in which the coefficients of Tn−1, Tn−2 and Tn−3 are prescribed has period 24 as a function of n, after a suitable normalization. A similar result holds over F5r, with the period being 60. We also show that this is a phenomena unique to characteristics 2 and 5. The result is strongly related to the supersingularity of certain curves associated with cyclotomic function fields, and in particular it complements an equidistribution result of Katz.
Symplectic ID
1145839
Favourite
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Publication type
Journal Article
Publication date
07 Dec 2018
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