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dc.contributor.authorKuo, Wentang
dc.contributor.authorLiu, Yu-Ru 15:10:07 (GMT) 15:10:07 (GMT)
dc.description.abstractLet A = 𝔽q[T] be the polynomial ring over the finite field 𝔽q, k = 𝔽q(T) the rational function field, and K a finite extension of k. Let Ļ• be a Drinfeld A-module over K of rank r. For a place 𝔓 of K of good reduction, write , where is the valuation ring of 𝔓 and its maximal ideal. Let P𝔓, Ļ•(X) be the characteristic polynomial of the Frobenius automorphism of 𝔽𝔓 acting on a Tate module of Ļ•. Let Ļ‡Ļ•(𝔓) = P𝔓, Ļ•(1), and let Ī½(Ļ‡Ļ•(𝔓)) be the number of distinct primes dividing Ļ‡Ļ•(𝔓). If Ļ• is of rank 2 with , we prove that there exists a normal distribution for the quantity For r ≥ 3, we show that the same result holds under the open image conjecture for Drinfeld modules. We also study the number of distinct prime divisors of the trace of the Frobenius automorphism of 𝔽𝔓 acting on a Tate module of Ļ• and obtain similar results.en
dc.publisherWorld Scientificen
dc.relation.ispartofseriesInternational Journal of Number Theory;5(7)
dc.subjectDrinfeld modulesen
dc.subjectnormal distributionen
dc.titleGaussian Laws on Drinfeld Modulesen
dcterms.bibliographicCitationKUO, W., & LIU, Y.-R. (2009). Gaussian laws on Drinfeld modules. International Journal of Number Theory, 05(07), 1179–1203.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Pure Mathematicsen

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