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On some properties of Carlitz cyclotomic polynomials. (English) Zbl 1385.11038

Summary: We consider the analogue, when \(\mathbb{Z}\) is replaced with \(\mathbb{F}_q [T]\) of the elementary cyclotomic polynomials and prove an analogue of Suzuki’s theorem.

MSC:

11G09 Drinfel’d modules; higher-dimensional motives, etc.
11T55 Arithmetic theory of polynomial rings over finite fields

Software:

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References:

[1] Bae, S., The arithmetic of Carlitz polynomials, J. Korean Math. Soc., 35, 341-360 (1998) · Zbl 0910.12001
[2] Goss, D., Basic Structures of Function Field Arithmetic, vol. 35 (1998), Springer
[3] Ji, C.; Li, W.; Moree, P., Values of coefficients of cyclotomic polynomials II, Discrete Math., 309, 1720-1723 (2009) · Zbl 1221.11067
[4] Stein, W., Sage Mathematics Software (2013), (version 5.6), The Sage Development Team
[5] Suzuki, J., On coefficients of cyclotomic polynomials, Proc. Japan Acad. Ser. A Math. Sci., 63, 279-280 (1987) · Zbl 0641.10008
[6] Weintraub, S. H., Several proofs of the irreducibility of the cyclotomic polynomials, Amer. Math. Monthly, 120, 537-545 (2013) · Zbl 1368.11023
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