Geodesic
Eisenstein's reciprocity law for Lubin–Tate formal groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 20, Tome 386 (2011), pp. 129-143 
S. V. Vostokov; M. A. Ivanov. Eisenstein's reciprocity law for Lubin–Tate formal groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 20, Tome 386 (2011), pp. 129-143. http://geodesic.mathdoc.fr/item/ZNSL_2011_386_a2/
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     author = {S. V. Vostokov and M. A. Ivanov},
     title = {Eisenstein's reciprocity law for {Lubin{\textendash}Tate} formal groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--143},
     year = {2011},
     volume = {386},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_386_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the present paper, we study a generalized norm residue symbol on Lubin–Tate formal groups and research a triviality for this symbol, when the first argument locate in the definition field of formal group. We use explicit formulas for the generalized norm residue symbol $(\ ,\,)_{F,n}$, herewith requirement, consisting of a bound to representing in the form uniformizing's degrees is removed. Bibl. 6 titles.

[1] G. Eisenstein, “Über ein einfaches Mittel zur Auffindung der höheren Reciprocitätsgesetze und der mit ihnen zu verbindenden Ergänzungssätze”, J. für die reine u. ang. Mathematik, 39 (1850), 351–364 | DOI | Zbl

[2] S. V. Vostokov, “Yavnaya forma zakona vzaimnosti”, Izv. AN SSSR. Ser. matem., 42:6 (1978), 1288–1321 | MR | Zbl

[3] S. V. Vostokov, “Normennoe sparivanie v formalnykh modulyakh”, Izv. AN SSSR. Ser. matem., 43:4 (1979), 765–794 | MR | Zbl

[4] I. B. Fesenko, S. V. Vostokov, Local Fields and Their Extensions, Second Edition, Amer. Math. Soc., Providence, R.I., 2002 | MR | Zbl

[5] Dzh. Kassels, A. Frëlikh (red.), Algebraicheskaya teoriya chisel, Mir, M., 1969 | MR

[6] S. V. Vostokov, M. A. Ivanov, G. K. Pak, “K odnoi rabote Khasse o zakone vzaimnosti Eizenshteina”, Zap. nauchn. semin. POMI, 365, 2009, 122–129 | MR | Zbl