Geodesic
Congruence modulo 2 of circular units in the fields $Q_{16}$ and $Q_{32}$
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 4, pp. 8-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the behavior of units (invertible elements) of the rings of integer of 2-circular fields is studied. In particular, the comparability of modulo 2 for the circular units of fields $Q_{16}$ и $Q_{32}$ is considered.
Keywords: group ring, group ring unit, cyclic group, primitive root. 
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R. Zh. Aleev; O. V. Mitina; E. A. Khristenko. Congruence modulo 2 of circular units in the fields $Q_{16}$ and $Q_{32}$. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 4, pp. 8-29. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_4_a1/

[1] R. Zh. Aleev, Tsentral'nye edinitsy tselochislennykh gruppovykh kolets konechnykh grupp, Chelyabinsk, 2000, 355 pp. (In Russ.)

[2] Ch. W. Curtis, I. Reiner, Representation Theory of Finite Groups and Associative Algebras, AMS Chelsea Publ., Providence, Rhode Island, 2006, 689 pp. | MR | MR | Zbl

[3] J. C. Miller, “Class numbers of totally real fields and applications to the Weber class number problem”, Acta Arithmetica, 164:4 (2014), 381–397 | DOI | MR | Zbl

[4] J. C. Miller, “Class numbers of real cyclotomic fields of composite conductor”, LMS J. of Computation and Mathematics, 17:A, special iss. (2014), 404–417 | DOI | MR

[5] F. J. van der Linden, “Class number computations of real Abelian number fields”, Mathematics of Computations, 39:160 (1982), 693–707 | DOI | MR | Zbl

[6] J. M. Masley, “Solution of small class number problems for cyclotomic fields”, Compositio Mathematica, 33:2 (1976), 179–186 | MR | Zbl

[7] T. Fukuda, K. Komatsu, “Weber's class number problem in the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}$”, III Intern. J. of Number Theory, 7:6 (2011), 1627–1635 | DOI | MR | Zbl

[8] R. Zh. Aleev, V. S. Taksheeva, “Generators of the group of cyclotomic units”, Bulletin of Chelyabinsk State University, 6 (107):10 (2008), 121–129 (In Russ.) | MR

[9] H. Bass, “Generators and relations for cyclotomic units”, Nagoya Mathematical J., 27:2 (1966), 401–407 | DOI | MR | Zbl

[10] I. M. Vinogradov, Fundamentals of number theory, Lan' Publ., St. Petersburg, 2009, 176 pp. (In Russ.)