Explicit reciprocity formulas in 2-adic number fields (Q1321747)

The author gives explicit formulas for the generalized Hilbert norm residue symbol on the field generated by prime-power division points of a Lubin-Tate formal group defined over \(k\), while \(k\) is a finite extension of the 2-adic rational number field. Consisting of complementary laws and general laws, these formulas are a 2-adic version of \textit{K. Shiratani's} in [RIMS Kokyuroku 658, 85-95 (1988; Zbl 0719.11069)], and are similar to those in the \(p\)-adic case for odd \(p\) in the author's [Mem. Fac. Sci. Kyushu Univ., Ser. A 47, 59- 70 (1993; Zbl 0792.11045)].