Geodesic
On explicit units in Kummer's tower
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 109-123 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider Kummer's tower, i. e. a family of number fields obtained by means of extracting all possible radicals from a rational base. We construct a few series of units in the tower where the base is equal to two and three. 
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     title = {On explicit units in {Kummer's} tower},
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A. L. Smirnov. On explicit units in Kummer's tower. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 109-123. http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a6/

[1] H. Wada, “A Table of Fundamental Units of Purely Cubic Fields”, Proc. Japan Acad., 46:10 (1970), 1135–1140 | DOI | MR | Zbl

[2] J. Coates, R. Sujatha, Cyclotomic Fields and Zeta Values, Monographs in Mathematics, Springer, 2006 | MR | Zbl

[3] G. Robert, “Unités elliptiques et formules pour le nombre de classes des extensions abéliennnes d'un corps quadratic imaginaire”, Bull. Soc. Math., France, 36 (1973), 5–77 | MR

[4] A. L. Smirnov, “Kummerova bashnya i bolshie dzeta-funktsii”, Zap. nauchn. sem. POMI, 469, 2018, 151–159

[5] G. Shimura, Yu. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Math. Soc. of Japan, 1961 | MR | Zbl