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oai:tokushima-u.repo.nii.ac.jp:02004106 2025-04-28T08:02:25Z 1713829974766:1713854679917:1716360593403 1713853213384:1713853297799

Hypothesis of Schinzel and Sierpiński and Cyclotomic Fields with Isomorphic Galois Groups 70194777 片山, 真一 カタヤマ, シンイチ Katayama, Shin-ichi 片山 カタヤマ Katayama 真一 シンイチ Shin-ichi open access In 1922 R. D. Carmichael conjectured that for any natural number n there exist infinitely many natural numbers m such that φ(n) = φ(m). It is well known that this conjecture can be proved under the assumption of the famous unproved hypothesis of Schinzel and Sierpiński. In this short note, we shall show the Hypothesis of Schinzel and Sierpiński implies more precisely that the existence of infinitely many cyclotomic fields Q(ζn) and Q(ζm) with isomorphic absolute Galois groups. Here ζn and ζm are primitive nth and mth roots of unity with m ≠ n. 2016 eng departmental bulletin paper VoR 322430 https://tokushima-u.repo.nii.ac.jp/records/2004106 13467387 AA11595324 Journal of Mathematics 50 43 47 https://tokushima-u.repo.nii.ac.jp/record/2004106/files/jm_50_43.pdf application/pdf 67 KB 2017-11-22