Geodesic
Generalized Artin--Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 233-259

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In the paper we consider the generalized Hilbert symbol in the cyclotomic extension of an absolutely unramified higher local field of characteristic 0 with perfect last residue field of characteristic $p>2$. We deduce the generalized Artin–Hasse and Iwasawa formulas from the explicit Kummer type Vostokov formula. 
@article{ZNSL_2002_289_a12,
     author = {A. N. Zinoviev},
     title = {Generalized {Artin--Hasse} and {Iwasawa} formulas for the {Hilbert} symbol in a higher local field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {233--259},
     publisher = {mathdoc},
     volume = {289},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a12/}
}
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A. N. Zinoviev. Generalized Artin--Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 233-259. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a12/