Amano, Fumiya On Rédei’s dihedral extension and triple reciprocity law. (English) Zbl 1286.11182 Proc. Japan Acad., Ser. A 90, No. 1, 1-5 (2014). Summary: In this paper, we give an arithmetic characterization of Rédei’s dihedral extension over \(\mathbb{Q}\) and another simple proof of the reciprocity law of the triple symbol. Cited in 5 Documents MSC: 11R32 Galois theory 11A15 Power residues, reciprocity Keywords:Rédei extension; Rédei triple symbol × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] B. J. Birch, Cyclotomic fields and Kummer extensions, in Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965) , 85-93, Thompson, Washington, DC., 1967. [2] I. B. Fesenko and S. V. Vostokov, Local fields and their extensions , 2nd ed., Translations of Mathematical Monographs, 121, Amer. Math. Soc., Providence, RI, 2002. · Zbl 1156.11046 [3] M. Morishita, On certain analogies between knots and primes, J. Reine Angew. Math. 550 (2002), 141-167. · Zbl 1065.57006 · doi:10.1515/crll.2002.070 [4] P. Morton, Density result for the \(2\)-classgroups of imaginary quadratic fields, J. Reine Angew. Math. 332 (1982), 156-187. · Zbl 0491.12004 · doi:10.1515/crll.1982.332.156 [5] T. Ono, An introduction to algebraic number theory , translated from the second Japanese edition by the author, The University Series in Mathematics, Plenum, New York, 1990. [6] L. Rédei, Ein neues zahlentheoretisches Symbol mit Anwendungen auf die Theorie der quadratischen Zahlkörper I, J. Reine Angew. Math. 180 (1939), 1-43. · Zbl 0021.00701 · doi:10.1515/crll.1939.180.1 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.