Geodesic
Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 46-60 
S. V. Vostokov; V. V. Volkov. Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 46-60. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a4/
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     author = {S. V. Vostokov and V. V. Volkov},
     title = {Explicit form of the {Hilbert} symbol on polynomial formal module for multidimensional local {field.~II}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Current paper describes the explicit formula of the Hibert pairing between Milnor $K$-group of multidimensional local field and polynomial formal module. This formula generalizes similar results for one-dimensioinal case and multidimensional case of multiplicative group. A case of different characteristics of a field and its first residue field is considered.

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