The second factor in the reciprocity law

The explicit formula for the symbol of the normed residue in a local field depends on the coefficients of two series. The second series is given by the choice of a prime element and a primitive root of unity. Recurrence relations are established in the work for the coefficients of this series which uniquely determine the series up to a factor from the ring of $p$-adic integers. Bibl. 3 titles.