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Irreducible polynomials over with three prescribed coefficients
For any positive integers and , we prove that the number
of monic irreducible polynomials of degree over in which
the coefficients of , and are prescribed has
period as a function of , after a suitable normalization. A similar
result holds over , with the period being . We also show
that this is a phenomena unique to characteristics and . 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.Comment: Incorporated referee comments. Accepted for publication in Finite
Fields App
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