Geodesic
Norm series in multidimensional local fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 60-83

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In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to a multidimensional local field. Necessary and sufficient conditions for the existence of norm series are obtained. 
@article{ZNSL_2003_305_a3,
     author = {S. V. Vostokov and G. K. Pak},
     title = {Norm series in multidimensional local fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--83},
     publisher = {mathdoc},
     volume = {305},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a3/}
}
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S. V. Vostokov; G. K. Pak. Norm series in multidimensional local fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 60-83. http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a3/